Two cards are drawn successively without replacement from a well‑shuffled standard deck of 52 cards. Given that the first card drawn is a heart, find the probability that the second card drawn is a king.
Answer
1/13
The correct answer is 1/13 — Simplify the numerator: (3+48)=51, so P=51/(13*51)=1/13.
Step-by-step solution
- There are 13 hearts in the deck; 1 of them is the king of hearts.
- Given the first card is a heart, two cases arise: (a) the first heart is the king of hearts (probability 1/13) leaving 3 kings in the remaining 51 cards; (b) the first heart is not a king (probability 12/13) leaving all 4 kings in the remaining 51 cards.
- Compute conditional probability: P= (1/13)*(3/51)+(12/13)*(4/51).
- Simplify the numerator: (3+48)=51, so P=51/(13*51)=1/13.
Common mistake: Ignoring the possibility that the first heart could be the king of hearts and using 4/51 directly.
Concept tested: Conditional probability without replacement
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