Question

2 In an experiment, the probability that event B occurs is and the probability that event A occurs given z' that event B occurs is 1. 4 What is the probability that events A and B both occur? Simplify any fractions.

Answer 1

Conditional probability

Initial explanation

We have that

- P(B) is the probability that event B occurs .

- P(A|B) is the probability that event A occurs given that event B occurs.

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

We have that:

`P\mleft(A|B\mright)=(P\mleft(A\cap B\mright))/(P(B))`

Since:

P(B) = 2/7

P(A|B) = 1/4

P(A∩B) =??

Then, replacing in the equation:

`P\mleft(A|B\mright)=(P\mleft(A\cap B\mright))/(P(B))`