{"id":3877,"date":"2023-06-01T14:47:32","date_gmt":"2023-06-01T14:47:32","guid":{"rendered":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/?post_type=chapter&#038;p=3877"},"modified":"2024-05-10T17:34:47","modified_gmt":"2024-05-10T17:34:47","slug":"probability-get-stronger","status":"publish","type":"chapter","link":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/chapter\/probability-get-stronger\/","title":{"raw":"Probability: Get Stronger","rendered":"Probability: Get Stronger"},"content":{"raw":"<ol start=\"1\">\r\n\t<li>A ball is drawn randomly from a jar that contains [latex]6[\/latex] red balls, [latex]2[\/latex] white balls, and [latex]5[\/latex] yellow balls. Find the probability of the given event.<br \/>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n\t<li>A red ball is drawn<\/li>\r\n\t<li>A white ball is drawn<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t<li>A group of people were asked if they had run a red light in the last year. [latex]150[\/latex] responded \"yes\", and [latex]185[\/latex] responded \"no\". Find the probability that if a person is chosen at random, they have run a red light in the last year.<\/li>\r\n\t<li>Compute the probability of tossing a six-sided die (with sides numbered [latex]1[\/latex] through [latex]6[\/latex]) and getting a [latex]5[\/latex].<\/li>\r\n\t<li>Giving a test to a group of students, the grades and gender are summarized below. If one student was chosen at random, find the probability that the student was female.<br \/>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>&nbsp;<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td>C<\/td>\r\n<td>Total<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Male<\/td>\r\n<td>[latex]8[\/latex]<\/td>\r\n<td>[latex]18[\/latex]<\/td>\r\n<td>[latex]13[\/latex]<\/td>\r\n<td>[latex]39[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Female<\/td>\r\n<td>[latex]10[\/latex]<\/td>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]12[\/latex]<\/td>\r\n<td>[latex]26[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Total<\/td>\r\n<td>[latex]18[\/latex]<\/td>\r\n<td>[latex]22[\/latex]<\/td>\r\n<td>[latex]25[\/latex]<\/td>\r\n<td>[latex]65[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n\t<li>Compute the probability of tossing a six-sided die and getting an even number.<\/li>\r\n\t<li>If you pick one card at random from a standard deck of cards, what is the probability it will be a King?<\/li>\r\n\t<li>Compute the probability of rolling a [latex]12[\/latex]-sided die and getting a number other than [latex]8[\/latex].<\/li>\r\n\t<li>Referring to the grade table from question #7, what is the probability that a student chosen at random did NOT earn a C?<\/li>\r\n\t<li>A six-sided die is rolled twice. What is the probability of showing a [latex]6[\/latex] on both rolls?<\/li>\r\n\t<li>A die is rolled twice. What is the probability of showing a [latex]5[\/latex] on the first roll and an even number on the second roll?<\/li>\r\n\t<li>Suppose a jar contains [latex]17[\/latex] red marbles and [latex]32[\/latex] blue marbles. If you reach in the jar and pull out [latex]2[\/latex] marbles at random, find the probability that both are red.<\/li>\r\n\t<li>Bert and Ernie each have a well-shuffled standard deck of [latex]52[\/latex] cards. They each draw one card from their own deck. Compute the probability that:<br \/>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n\t<li>Bert and Ernie both draw an Ace.<\/li>\r\n\t<li>Bert draws an Ace but Ernie does not.<\/li>\r\n\t<li>neither Bert nor Ernie draws an Ace.<\/li>\r\n\t<li>Bert and Ernie both draw a heart.<\/li>\r\n\t<li>Bert gets a card that is not a Jack and Ernie draws a card that is not a heart.<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t<li>Compute the probability of drawing a King from a deck of cards and then drawing a Queen.<\/li>\r\n\t<li>A math class consists of [latex]25[\/latex] students, [latex]14[\/latex] female and [latex]11[\/latex] male.\u00a0 Two students are selected at random to participate in a probability experiment.\u00a0 Compute the probability that<br \/>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n\t<li>a male is selected, then a female.<\/li>\r\n\t<li>a female is selected, then a male.<\/li>\r\n\t<li>two males are selected.<\/li>\r\n\t<li>two females are selected.<\/li>\r\n\t<li>no males are selected.<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t<li>Giving a test to a group of students, the grades and gender are summarized below. If one student was chosen at random, find the probability that the student was female and earned an A.<br \/>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td>&nbsp;<\/td>\r\n<td>A<\/td>\r\n<td>B<\/td>\r\n<td>C<\/td>\r\n<td>Total<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Male<\/td>\r\n<td>[latex]8[\/latex]<\/td>\r\n<td>[latex]18[\/latex]<\/td>\r\n<td>[latex]13[\/latex]<\/td>\r\n<td>[latex]39[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Female<\/td>\r\n<td>[latex]10[\/latex]<\/td>\r\n<td>[latex]4[\/latex]<\/td>\r\n<td>[latex]12[\/latex]<\/td>\r\n<td>[latex]26[\/latex]<\/td>\r\n<\/tr>\r\n<tr>\r\n<td>Total<\/td>\r\n<td>[latex]18[\/latex]<\/td>\r\n<td>[latex]22[\/latex]<\/td>\r\n<td>[latex]25[\/latex]<\/td>\r\n<td>[latex]65[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/li>\r\n\t<li>A jar contains [latex]6[\/latex] red marbles numbered [latex]1[\/latex] to [latex]6[\/latex] and [latex]8[\/latex] blue marbles numbered [latex]1[\/latex] to [latex]8[\/latex]. A marble is drawn at random from the jar. Find the probability the marble is red or odd-numbered.<\/li>\r\n\t<li>Referring to the table from #29, find the probability that a student chosen at random is female or earned a B.<\/li>\r\n\t<li>Compute the probability of drawing the King of hearts or a Queen from a deck of cards.<\/li>\r\n\t<li>A jar contains [latex]5[\/latex] red marbles numbered [latex]1[\/latex] to [latex]5[\/latex] and [latex]8 [\/latex] blue marbles numbered [latex]1[\/latex] to [latex]8[\/latex]. A marble is drawn at random from the jar. Find the probability the marble is<br \/>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n\t<li>Even-numbered given that the marble is red.<\/li>\r\n\t<li>Red given that the marble is even-numbered.<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t<li>Compute the probability of flipping a coin and getting heads, given that the previous flip was tails.<\/li>\r\n\t<li>Suppose a math class contains [latex]25[\/latex] students, [latex]14[\/latex] females (three of whom speak French) and [latex]11[\/latex] males (two of whom speak French). Compute the probability that a randomly selected student speaks French, given that the student is female.<\/li>\r\n\t<li>A certain virus infects one in every [latex]400[\/latex] people. A test used to detect the virus in a person is positive [latex]90\\%[\/latex] of the time if the person has the virus and [latex]10\\%[\/latex] of the time if the person does not have the virus. Let A be the event \"the person is infected\" and B be the event \"the person tests positive\".<br \/>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n\t<li>Find the probability that a person has the virus given that they have tested positive, i.e. find P(A | B).<\/li>\r\n\t<li>Find the probability that a person does not have the virus given that they test negative, i.e. find P(not A | not B).<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t<li>A certain disease has an incidence rate of [latex]0.3\\%[\/latex]. If the false negative rate is [latex]6\\%[\/latex] and the false positive rate is [latex]4\\%[\/latex], compute the probability that a person who tests positive actually has the disease.<\/li>\r\n\t<li>A certain group of symptom-free women between the ages of [latex]40[\/latex] and [latex]50[\/latex] are randomly selected to participate in mammography screening.\u00a0 The incidence rate of breast cancer among such women is [latex]0.8\\%[\/latex].\u00a0 The false negative rate for the mammogram is [latex]10\\%[\/latex].\u00a0 The false positive rate is [latex]7\\%[\/latex].\u00a0 If a the mammogram results for a particular woman are positive (indicating that she has breast cancer), what is the probability that she actually has breast cancer?<\/li>\r\n\t<li>A boy owns [latex]2[\/latex] pairs of pants, [latex]3[\/latex] shirts, [latex]8[\/latex] ties, and [latex]2[\/latex] jackets. How many different outfits can he wear to school if he must wear one of each item?<\/li>\r\n\t<li>How many three-letter \"words\" can be made from [latex]4[\/latex] letters \"FGHI\" if<br \/>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n\t<li>repetition of letters is allowed<\/li>\r\n\t<li>repetition of letters is not allowed<\/li>\r\n<\/ol>\r\n<\/li>\r\n\t<li>All of the license plates in a particular state feature three letters followed by three digits (e.g. [latex]ABC 123[\/latex]). How many different license plate numbers are available to the state's Department of Motor Vehicles?<\/li>\r\n\t<li>A pianist plans to play [latex]4[\/latex] pieces at a recital. In how many ways can she arrange these pieces in the program?<\/li>\r\n\t<li>Seven Olympic sprinters are eligible to compete in the [latex]4[\/latex] x [latex]100[\/latex] m relay race for the USA Olympic team. How many four-person relay teams can be selected from among the seven athletes?<\/li>\r\n\t<li>In western music, an octave is divided into [latex]12[\/latex] pitches.\u00a0 For the film <em>Close Encounters of the Third Kind<\/em>, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth.\u00a0 Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?<\/li>\r\n\t<li>In how many ways can [latex]4[\/latex] pizza toppings be chosen from [latex]12[\/latex] available toppings?<\/li>\r\n\t<li>In the [latex]6\/50[\/latex] lottery game, a player picks six numbers from [latex]1[\/latex] to [latex]50[\/latex]. How many different choices does the player have if order doesn\u2019t matter?<\/li>\r\n\t<li>A jury pool consists of [latex]27[\/latex] people. How many different ways can [latex]11[\/latex] people be chosen to serve on a jury and one additional person be chosen to serve as the jury foreman?<\/li>\r\n\t<li>You own [latex]16[\/latex] CDs. You want to randomly arrange [latex]5[\/latex] of them in a CD rack. What is the probability that the rack ends up in alphabetical order?<\/li>\r\n\t<li>In a lottery game, a player picks six numbers from [latex]1[\/latex] to [latex]48[\/latex]. If [latex]5[\/latex] of the [latex]6[\/latex] numbers match those drawn, they player wins second prize. What is the probability of winning this prize?<\/li>\r\n\t<li>Compute the probability that a [latex]5[\/latex]-card poker hand is dealt to you that contains all hearts.<\/li>\r\n\t<li>A bag contains [latex]3[\/latex] gold marbles, [latex]6[\/latex] silver marbles, and [latex]28[\/latex] black marbles. Someone offers to play this game: You randomly select on marble from the bag. If it is gold, you win [latex]$3[\/latex]. If it is silver, you win [latex]$2[\/latex]. If it is black, you lose [latex]$1[\/latex]. What is your expected value if you play this game?<\/li>\r\n\t<li>In a lottery game, a player picks six numbers from [latex]1[\/latex] to [latex]23[\/latex]. If the player matches all six numbers, they win [latex]30,000[\/latex] dollars. Otherwise, they lose [latex]$1[\/latex]. Find the expected value of this game.<\/li>\r\n\t<li>A company estimates that [latex]0.7%[\/latex] of their products will fail after the original warranty period but within [latex]2[\/latex] years of the purchase, with a replacement cost of [latex]$350[\/latex]. If they offer a [latex]2[\/latex] year extended warranty for [latex]$48[\/latex], what is the company's expected value of each warranty sold?<\/li>\r\n<\/ol>","rendered":"<ol start=\"1\">\n<li>A ball is drawn randomly from a jar that contains [latex]6[\/latex] red balls, [latex]2[\/latex] white balls, and [latex]5[\/latex] yellow balls. Find the probability of the given event.\n<ol style=\"list-style-type: lower-alpha;\">\n<li>A red ball is drawn<\/li>\n<li>A white ball is drawn<\/li>\n<\/ol>\n<\/li>\n<li>A group of people were asked if they had run a red light in the last year. [latex]150[\/latex] responded &#8220;yes&#8221;, and [latex]185[\/latex] responded &#8220;no&#8221;. Find the probability that if a person is chosen at random, they have run a red light in the last year.<\/li>\n<li>Compute the probability of tossing a six-sided die (with sides numbered [latex]1[\/latex] through [latex]6[\/latex]) and getting a [latex]5[\/latex].<\/li>\n<li>Giving a test to a group of students, the grades and gender are summarized below. If one student was chosen at random, find the probability that the student was female.<br \/>\n<table>\n<tbody>\n<tr>\n<td>&nbsp;<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td>C<\/td>\n<td>Total<\/td>\n<\/tr>\n<tr>\n<td>Male<\/td>\n<td>[latex]8[\/latex]<\/td>\n<td>[latex]18[\/latex]<\/td>\n<td>[latex]13[\/latex]<\/td>\n<td>[latex]39[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Female<\/td>\n<td>[latex]10[\/latex]<\/td>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]12[\/latex]<\/td>\n<td>[latex]26[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Total<\/td>\n<td>[latex]18[\/latex]<\/td>\n<td>[latex]22[\/latex]<\/td>\n<td>[latex]25[\/latex]<\/td>\n<td>[latex]65[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>Compute the probability of tossing a six-sided die and getting an even number.<\/li>\n<li>If you pick one card at random from a standard deck of cards, what is the probability it will be a King?<\/li>\n<li>Compute the probability of rolling a [latex]12[\/latex]-sided die and getting a number other than [latex]8[\/latex].<\/li>\n<li>Referring to the grade table from question #7, what is the probability that a student chosen at random did NOT earn a C?<\/li>\n<li>A six-sided die is rolled twice. What is the probability of showing a [latex]6[\/latex] on both rolls?<\/li>\n<li>A die is rolled twice. What is the probability of showing a [latex]5[\/latex] on the first roll and an even number on the second roll?<\/li>\n<li>Suppose a jar contains [latex]17[\/latex] red marbles and [latex]32[\/latex] blue marbles. If you reach in the jar and pull out [latex]2[\/latex] marbles at random, find the probability that both are red.<\/li>\n<li>Bert and Ernie each have a well-shuffled standard deck of [latex]52[\/latex] cards. They each draw one card from their own deck. Compute the probability that:\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Bert and Ernie both draw an Ace.<\/li>\n<li>Bert draws an Ace but Ernie does not.<\/li>\n<li>neither Bert nor Ernie draws an Ace.<\/li>\n<li>Bert and Ernie both draw a heart.<\/li>\n<li>Bert gets a card that is not a Jack and Ernie draws a card that is not a heart.<\/li>\n<\/ol>\n<\/li>\n<li>Compute the probability of drawing a King from a deck of cards and then drawing a Queen.<\/li>\n<li>A math class consists of [latex]25[\/latex] students, [latex]14[\/latex] female and [latex]11[\/latex] male.\u00a0 Two students are selected at random to participate in a probability experiment.\u00a0 Compute the probability that\n<ol style=\"list-style-type: lower-alpha;\">\n<li>a male is selected, then a female.<\/li>\n<li>a female is selected, then a male.<\/li>\n<li>two males are selected.<\/li>\n<li>two females are selected.<\/li>\n<li>no males are selected.<\/li>\n<\/ol>\n<\/li>\n<li>Giving a test to a group of students, the grades and gender are summarized below. If one student was chosen at random, find the probability that the student was female and earned an A.<br \/>\n<table>\n<tbody>\n<tr>\n<td>&nbsp;<\/td>\n<td>A<\/td>\n<td>B<\/td>\n<td>C<\/td>\n<td>Total<\/td>\n<\/tr>\n<tr>\n<td>Male<\/td>\n<td>[latex]8[\/latex]<\/td>\n<td>[latex]18[\/latex]<\/td>\n<td>[latex]13[\/latex]<\/td>\n<td>[latex]39[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Female<\/td>\n<td>[latex]10[\/latex]<\/td>\n<td>[latex]4[\/latex]<\/td>\n<td>[latex]12[\/latex]<\/td>\n<td>[latex]26[\/latex]<\/td>\n<\/tr>\n<tr>\n<td>Total<\/td>\n<td>[latex]18[\/latex]<\/td>\n<td>[latex]22[\/latex]<\/td>\n<td>[latex]25[\/latex]<\/td>\n<td>[latex]65[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/li>\n<li>A jar contains [latex]6[\/latex] red marbles numbered [latex]1[\/latex] to [latex]6[\/latex] and [latex]8[\/latex] blue marbles numbered [latex]1[\/latex] to [latex]8[\/latex]. A marble is drawn at random from the jar. Find the probability the marble is red or odd-numbered.<\/li>\n<li>Referring to the table from #29, find the probability that a student chosen at random is female or earned a B.<\/li>\n<li>Compute the probability of drawing the King of hearts or a Queen from a deck of cards.<\/li>\n<li>A jar contains [latex]5[\/latex] red marbles numbered [latex]1[\/latex] to [latex]5[\/latex] and [latex]8[\/latex] blue marbles numbered [latex]1[\/latex] to [latex]8[\/latex]. A marble is drawn at random from the jar. Find the probability the marble is\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Even-numbered given that the marble is red.<\/li>\n<li>Red given that the marble is even-numbered.<\/li>\n<\/ol>\n<\/li>\n<li>Compute the probability of flipping a coin and getting heads, given that the previous flip was tails.<\/li>\n<li>Suppose a math class contains [latex]25[\/latex] students, [latex]14[\/latex] females (three of whom speak French) and [latex]11[\/latex] males (two of whom speak French). Compute the probability that a randomly selected student speaks French, given that the student is female.<\/li>\n<li>A certain virus infects one in every [latex]400[\/latex] people. A test used to detect the virus in a person is positive [latex]90\\%[\/latex] of the time if the person has the virus and [latex]10\\%[\/latex] of the time if the person does not have the virus. Let A be the event &#8220;the person is infected&#8221; and B be the event &#8220;the person tests positive&#8221;.\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Find the probability that a person has the virus given that they have tested positive, i.e. find P(A | B).<\/li>\n<li>Find the probability that a person does not have the virus given that they test negative, i.e. find P(not A | not B).<\/li>\n<\/ol>\n<\/li>\n<li>A certain disease has an incidence rate of [latex]0.3\\%[\/latex]. If the false negative rate is [latex]6\\%[\/latex] and the false positive rate is [latex]4\\%[\/latex], compute the probability that a person who tests positive actually has the disease.<\/li>\n<li>A certain group of symptom-free women between the ages of [latex]40[\/latex] and [latex]50[\/latex] are randomly selected to participate in mammography screening.\u00a0 The incidence rate of breast cancer among such women is [latex]0.8\\%[\/latex].\u00a0 The false negative rate for the mammogram is [latex]10\\%[\/latex].\u00a0 The false positive rate is [latex]7\\%[\/latex].\u00a0 If a the mammogram results for a particular woman are positive (indicating that she has breast cancer), what is the probability that she actually has breast cancer?<\/li>\n<li>A boy owns [latex]2[\/latex] pairs of pants, [latex]3[\/latex] shirts, [latex]8[\/latex] ties, and [latex]2[\/latex] jackets. How many different outfits can he wear to school if he must wear one of each item?<\/li>\n<li>How many three-letter &#8220;words&#8221; can be made from [latex]4[\/latex] letters &#8220;FGHI&#8221; if\n<ol style=\"list-style-type: lower-alpha;\">\n<li>repetition of letters is allowed<\/li>\n<li>repetition of letters is not allowed<\/li>\n<\/ol>\n<\/li>\n<li>All of the license plates in a particular state feature three letters followed by three digits (e.g. [latex]ABC 123[\/latex]). How many different license plate numbers are available to the state&#8217;s Department of Motor Vehicles?<\/li>\n<li>A pianist plans to play [latex]4[\/latex] pieces at a recital. In how many ways can she arrange these pieces in the program?<\/li>\n<li>Seven Olympic sprinters are eligible to compete in the [latex]4[\/latex] x [latex]100[\/latex] m relay race for the USA Olympic team. How many four-person relay teams can be selected from among the seven athletes?<\/li>\n<li>In western music, an octave is divided into [latex]12[\/latex] pitches.\u00a0 For the film <em>Close Encounters of the Third Kind<\/em>, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth.\u00a0 Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?<\/li>\n<li>In how many ways can [latex]4[\/latex] pizza toppings be chosen from [latex]12[\/latex] available toppings?<\/li>\n<li>In the [latex]6\/50[\/latex] lottery game, a player picks six numbers from [latex]1[\/latex] to [latex]50[\/latex]. How many different choices does the player have if order doesn\u2019t matter?<\/li>\n<li>A jury pool consists of [latex]27[\/latex] people. How many different ways can [latex]11[\/latex] people be chosen to serve on a jury and one additional person be chosen to serve as the jury foreman?<\/li>\n<li>You own [latex]16[\/latex] CDs. You want to randomly arrange [latex]5[\/latex] of them in a CD rack. What is the probability that the rack ends up in alphabetical order?<\/li>\n<li>In a lottery game, a player picks six numbers from [latex]1[\/latex] to [latex]48[\/latex]. If [latex]5[\/latex] of the [latex]6[\/latex] numbers match those drawn, they player wins second prize. What is the probability of winning this prize?<\/li>\n<li>Compute the probability that a [latex]5[\/latex]-card poker hand is dealt to you that contains all hearts.<\/li>\n<li>A bag contains [latex]3[\/latex] gold marbles, [latex]6[\/latex] silver marbles, and [latex]28[\/latex] black marbles. Someone offers to play this game: You randomly select on marble from the bag. If it is gold, you win [latex]$3[\/latex]. If it is silver, you win [latex]$2[\/latex]. If it is black, you lose [latex]$1[\/latex]. What is your expected value if you play this game?<\/li>\n<li>In a lottery game, a player picks six numbers from [latex]1[\/latex] to [latex]23[\/latex]. If the player matches all six numbers, they win [latex]30,000[\/latex] dollars. Otherwise, they lose [latex]$1[\/latex]. Find the expected value of this game.<\/li>\n<li>A company estimates that [latex]0.7%[\/latex] of their products will fail after the original warranty period but within [latex]2[\/latex] years of the purchase, with a replacement cost of [latex]$350[\/latex]. If they offer a [latex]2[\/latex] year extended warranty for [latex]$48[\/latex], what is the company&#8217;s expected value of each warranty sold?<\/li>\n<\/ol>\n","protected":false},"author":15,"menu_order":20,"template":"","meta":{"_candela_citation":"[]","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"part":76,"module-header":"practice","content_attributions":[],"internal_book_links":[],"video_content":null,"cc_video_embed_content":{"cc_scripts":"","media_targets":[]},"try_it_collection":null,"_links":{"self":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/3877"}],"collection":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/users\/15"}],"version-history":[{"count":18,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/3877\/revisions"}],"predecessor-version":[{"id":14310,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/3877\/revisions\/14310"}],"part":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/parts\/76"}],"metadata":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapters\/3877\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/media?parent=3877"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/pressbooks\/v2\/chapter-type?post=3877"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/contributor?post=3877"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/content.one.lumenlearning.com\/quantitativereasoning\/wp-json\/wp\/v2\/license?post=3877"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}