Question

PLEASE HELP ME with an explanation. Thanks in advance

Answer 1

Option 3.

Explanation:

Let T=Total, B=Brother and S=Sister. By using given diagram, we get

`n(B)=28+68=96`

`n(S)=82+68=150`

`n(T)=28+68+82+52=230`

`n(B\cap S)=68`

Using this information, we get

`P(B)=(n(B))/(n(T))=(96)/(230)\approx 0.42`

`P(S)=(n(S))/(n(T))=(150)/(230)\approx 0.65`

`P(S|B)=(P(B\cap S))/(P(B))=(n(B\cap S))/(n(B))=(68)/(96)\approx 0.71`

`P(B|S)=(P(B\cap S))/(P(S))=(n(B\cap S))/(n(S))=(68)/(150)\approx 0.45`

The probability P(S|B) has the largest value.

Therefore, the correct option is 3.