SAT Probability and conditional probability Practice Question 12 (Hard)

Question bank / Probability and conditional probability

Math · Problem-Solving and Data AnalysisHard

Five cards are numbered $1$ through $5$ . Two cards are drawn at random, one after the other, without replacement. What is the probability that both cards drawn show even numbers?

$\frac{4}{25}$

$\frac{1}{10}$

$\frac{1}{5}$

$\frac{2}{5}$

Show answer and explanation

Answer: B

There are $2$ even cards ( $2$ and $4$ ) among $5$ . The probability that the first card is even is $\frac{2}{5}$ . Given that, $1$ even card remains among $4$ , so the probability that the second is even is $\frac{1}{4}$ . Multiply: $\frac{2}{5} \cdot \frac{1}{4} = \frac{1}{10}$ .

Choice A, $\frac{2}{5} \cdot \frac{2}{5}$ , treats the draws as if the first card were replaced.

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