- Of the cars on a used car lot, $70 \%$ have air conditioning $(A C)$ and $40 \%$ have a $C D$ player (CD). $20 \%$ of the cars have both.
What is the probability that a car has a CD player, given that it has AC?

Answer

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Answer

$\boxed{0.286}$ or $\boxed{28.6\%}$ is the probability that a car has a CD player, given that it has AC

Steps

Step 1 ：Given probabilities: P(AC) = 0.7, P(CD) = 0.4, P(CD ∩ AC) = 0.2

Step 2 ：Use the conditional probability formula: P(CD | AC) = $\frac{P(CD \cap AC)}{P(AC)}$

Step 3 ：Plug in the values: P(CD | AC) = $\frac{0.2}{0.7}$

Step 4 ：Calculate the probability: P(CD | AC) ≈ 0.286

Step 5 ：$\boxed{0.286}$ or $\boxed{28.6\%}$ is the probability that a car has a CD player, given that it has AC