select the correct answer.\nconsider event a and event b. what is the probability that event b occurs, given…

select the correct answer.\nconsider event a and event b. what is the probability that event b occurs, given that event a has already occurred?\na. $\frac{p(bcap a)}{p(a)cdot p(b)}$\nb. $\frac{p(bcap a)}{p(a)}$\nc. $\frac{p(bcap a)}{p(b)}$\nd. $\frac{p(bcup a)}{p(b)}$

select the correct answer.\nconsider event a and event b. what is the probability that event b occurs, given that event a has already occurred?\na. $\frac{p(bcap a)}{p(a)cdot p(b)}$\nb. $\frac{p(bcap a)}{p(a)}$\nc. $\frac{p(bcap a)}{p(b)}$\nd. $\frac{p(bcup a)}{p(b)}$

Answer

Explanation:

Step1: Recall conditional - probability formula

The formula for the conditional probability of event $B$ given event $A$ is $P(B|A)=\frac{P(B\cap A)}{P(A)}$, where $P(B|A)$ is the probability that event $B$ occurs given that event $A$ has already occurred, $P(B\cap A)$ is the probability of both $A$ and $B$ occurring, and $P(A)$ is the probability of event $A$ occurring.

Answer:

B. $\frac{P(B\cap A)}{P(A)}$