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

Answer:

A. 0.5313

B. 0.15

Step-by-step 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

$P(A|B)=\dfrac{P(A\cap B)}{P(B)}\\ \\P(A|B)=\dfrac{0.17}{0.32}=\dfrac{17}{32}=0.53125\approx 0.5313$

B. Use formula

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