Exercise · ZW-LAW-OF-TOTAL-PROBABILITY-006 · ★★☆ Intermediate
Two cards are drawn without replacement from a 52-card deck. What is the probability that the second is an ace?
Choose one option.
Show answer
- C. 1/13
Explanation
Conditioning on whether the first was an ace: \(\tfrac4{52}\cdot\tfrac3{51}+\tfrac{48}{52}\cdot\tfrac4{51}=\tfrac1{13}\), the same as for the first card.
Review the concept: Law of total probability
The total probability of an event \(A\) is the weighted average of its conditional probabilities \(P(A\mid B_i)\) over a partition \(B_i\) of the sample space, with the probability of each case as its weight.
\[P(A)=\sum_{i=1}^{n}P(A\mid B_i)\,P(B_i)\]
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