can someone explain the last stepthe last line In rolling a

can someone explain the last step(the last line)...

In rolling a die, what is the probability of getting an even number, given that it is a prime number?

Solution

Sample Space S is

S={1,2,3,4,5,6}

And A represent Event of even number which is

A={2,4,6}

And B is an event of prime number which is

B={1,3,5}

We have to find the probability of getting aneven number given that it is a prime. Such probability is known as conditional probability where probability of getting an event depends on another probability and is represented by

P(A/B) = P(A intersection B)/P(B)

And P(A intersection B)=1/6

And P(B)=3/6=

Therefore P(A/B) = P(A intersection B)/P(B)

              P(A/B) = (1/6/3/6) =1/3