Mathematics: 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

40=10+2x where x is the number of dogs.30=2xx=15Therefore she must walk 15 dogsHope this helps :)...

If p(a)=.55, p(b)=.32 and p(aub)=.70, a. find p(a|b)

kpruitt6359

07.01.2022

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

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

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