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Five bad apples are mixed with 15 good apples accidently. Let the random variable X be the number of bad apples in a draw of two apples, then mean of X is

Solution

✅ Correct Option: 4

P(X=0)=(152)(202)=105190P(X=0)=\frac{\binom{15}{2}}{\binom{20}{2}}=\frac{105}{190}, P(X=1)=75190P(X=1)=\frac{75}{190}, P(X=2)=10190P(X=2)=\frac{10}{190}.

Mean =75+20190=95190=12=\frac{75+20}{190}=\frac{95}{190}=\frac12.

More quickly, by linearity each of the 22 draws is bad with probability 520\frac{5}{20}, so E(X)=2×14=12E(X)=2\times\frac14=\frac12.

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