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.
A red ball is drawn
A white ball is drawn
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.
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].
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.
A
B
C
Total
Male
[latex]8[/latex]
[latex]18[/latex]
[latex]13[/latex]
[latex]39[/latex]
Female
[latex]10[/latex]
[latex]4[/latex]
[latex]12[/latex]
[latex]26[/latex]
Total
[latex]18[/latex]
[latex]22[/latex]
[latex]25[/latex]
[latex]65[/latex]
Compute the probability of tossing a six-sided die and getting an even number.
If you pick one card at random from a standard deck of cards, what is the probability it will be a King?
Compute the probability of rolling a [latex]12[/latex]-sided die and getting a number other than [latex]8[/latex].
Referring to the grade table from question #7, what is the probability that a student chosen at random did NOT earn a C?
A six-sided die is rolled twice. What is the probability of showing a [latex]6[/latex] on both rolls?
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?
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.
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:
Bert and Ernie both draw an Ace.
Bert draws an Ace but Ernie does not.
neither Bert nor Ernie draws an Ace.
Bert and Ernie both draw a heart.
Bert gets a card that is not a Jack and Ernie draws a card that is not a heart.
Compute the probability of drawing a King from a deck of cards and then drawing a Queen.
A math class consists of [latex]25[/latex] students, [latex]14[/latex] female and [latex]11[/latex] male. Two students are selected at random to participate in a probability experiment. Compute the probability that
a male is selected, then a female.
a female is selected, then a male.
two males are selected.
two females are selected.
no males are selected.
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.
A
B
C
Total
Male
[latex]8[/latex]
[latex]18[/latex]
[latex]13[/latex]
[latex]39[/latex]
Female
[latex]10[/latex]
[latex]4[/latex]
[latex]12[/latex]
[latex]26[/latex]
Total
[latex]18[/latex]
[latex]22[/latex]
[latex]25[/latex]
[latex]65[/latex]
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.
Referring to the table from #29, find the probability that a student chosen at random is female or earned a B.
Compute the probability of drawing the King of hearts or a Queen from a deck of cards.
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
Even-numbered given that the marble is red.
Red given that the marble is even-numbered.
Compute the probability of flipping a coin and getting heads, given that the previous flip was tails.
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.
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”.
Find the probability that a person has the virus given that they have tested positive, i.e. find P(A | B).
Find the probability that a person does not have the virus given that they test negative, i.e. find P(not A | not B).
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.
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. The incidence rate of breast cancer among such women is [latex]0.8\%[/latex]. The false negative rate for the mammogram is [latex]10\%[/latex]. The false positive rate is [latex]7\%[/latex]. 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?
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?
How many three-letter “words” can be made from [latex]4[/latex] letters “FGHI” if
repetition of letters is allowed
repetition of letters is not allowed
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?
A pianist plans to play [latex]4[/latex] pieces at a recital. In how many ways can she arrange these pieces in the program?
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?
In western music, an octave is divided into [latex]12[/latex] pitches. For the film Close Encounters of the Third Kind, director Steven Spielberg asked composer John Williams to write a five-note theme, which aliens would use to communicate with people on Earth. Disregarding rhythm and octave changes, how many five-note themes are possible if no note is repeated?
In how many ways can [latex]4[/latex] pizza toppings be chosen from [latex]12[/latex] available toppings?
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’t matter?
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?
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?
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?
Compute the probability that a [latex]5[/latex]-card poker hand is dealt to you that contains all hearts.
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?
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.
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?