## Related questions with answers

Question

In a car rental company 's fleet, 70% of the cars are American brands, 20% are Japanese, and the rest are German. The company notes that manufacturers' recalls seem to affect 2% of the American cars, but only 1% of the others.

What's the probability that a recalled car is American?

Solution

VerifiedAnswered 7 months ago

Answered 7 months ago

Step 1

1 of 4Let $A$="American" and $J$="Japanese" and $G$="German" and $B$="recall"

$\begin{aligned} P(A)&=70\%=0.7 \\ P(J)&=20\%=0.2 \\ P(G)&=10\%=0.1 \\ P(B|A)&=2\%=0.02 \\ P(B|J)&=1\%=0.01 \\ P(B|G)&=1\%=0.01 \end{aligned}$

General multiplication rule:

$P(A\text{ and }B)=P(A\cap B)=P(A)\times P(B|A)=P(B)\times P(A|B)$

Definition Conditional probability:

$P(B|A)=\dfrac{P(A\cap B)}{P(A)}=\dfrac{P(A\text{ and }B)}{P(A)}$

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