Question

From the sample space S=(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15) a single number is to be selected at random. Given event A, that the selected number is even, and event B, that the selected number is a multiple of 4, find P(AIB)​

Answer 1

`P(A|B) = 1`

Explanation:

Given

`S = \{1,2,3,4,5,6,7,8,9,10,11,12,13,14,15\}`

`A = \{2,4,6,8,10,12,14\}`

`P(A) = 7/15`

`B = \{4,8,12\}`

`P(B) = 3/15`

Required

`P(A|B)`

This is calculated as:

`P(A|B) = (P(A\ n\ B))/(P(B))`

Where

`A\ n\ B = \{4,8,12\}`

`P(A\ n\ B) = 3/15`

So, we have:

`P(A|B) = (P(A\ n\ B))/(P(B))`

`P(A|B) = (3/15)/(3/15)`

`P(A|B) = 1`