Question

What is the probability that A occurs given that B occurs ?

Answer 1

This is an instance of conditional probability and the formula to use is;

`P(\text{AIB)}=(P(A\cap B))/(P(B))`

Where:

P(A|B) = the probability of event A occurring given that event B occurred

P(A ∩ B) = the probability that both events A and B occur

P(B) = the probability of event B

`\begin{gathered} P(\text{AnB)}=(1)/(3) \\ P(B)=(2)/(5) \end{gathered}`
`P(\text{AIB)}=((1)/(3))/((2)/(5))=(1)/(3)*(5)/(2)=(5)/(6)`

Therefore, the probability that A occurs given that B occurs is 5/6