Question

If P(A)=.55, P(B)=.32 And P(AuB)=.70,

A. Find P(A|B) round to 4 decimal places

B. Find P(A’|B)
Round to 4 decimal places

Answer 1

A. 0.5313

B. 0.15

Explanation:

Given:

`P(A)=0.55\\ \\P(B)=0.32\\ \\P(A\cup B)=0.70`

First , use formula

`P(A\cup B)=P(A)+P(B)-P(A\cap B)`

to find
`P(A\cap B):`

`0.70=0.55+0.32-P(A\cap B)\\ \\P(A\cap B)=0.55+0.32-0.70=0.87-0.70=0.17`

A. Use formula

`P(A|B)=(P(A\cap B))/(P(B))\\ \\P(A|B)=(0.17)/(0.32)=(17)/(32)=0.53125\approx 0.5313`

B. Use formula

`P(A'|B)=P(B)-P(A\cap B)=0.32-0.17=0.15`