- Calculate and interpret probabilities of simple and compound events.
- Describe the meaning of mutually exclusive and independence using probability
Probability Properties
You can always use the following formula to find the probability:
[latex]P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)[/latex]
probability properties
- For any two events, [latex]A[/latex] and [latex]B[/latex]: [latex]P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B)[/latex]
- Two events are mutually exclusive if the probability that they both happen at the same time is zero. That is, if events [latex]A[/latex] and [latex]B[/latex] are mutually exclusive, then [latex]P(A \ \mathrm{and} \ B) = 0[/latex].
Therefore, [latex]P(A \text{ or } B) = P(A) + P(B) - P(A \text{ and } B) = P(A) + P(B) - 0 = P(A) + P(B)[/latex]
- Two events are independent if [latex]P(A \text{ and } B )= P(A)\times P(B)[/latex]
The availability of a safe and effective vaccine for COVID-19 is a well-recognized additional tool contributing to the control of the COVID-19 pandemic. At the same time, the challenges and efforts needed to rapidly develop, evaluate, and produce this at scale are enormous.[1] Based on all of the research done so far, COVID-19 vaccines can offer added protection to people who had COVID-19, including protection against being hospitalized from a new infection, especially as variants continue to emerge. Now is the time for global solidarity and support, because only together can we overcome the intertwined health, social, and economic impacts of the pandemic. Only then can we protect the health, livelihoods, food security, and nutrition of all people, and ensure that our ‘new normal’ is a better one.[2]