在南北家有8張黑桃的情況下西家剛好有一張的機率

Question

在南北家有8張黑桃的情況下 西家剛好有一張的機率

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ 我們已知南、北家共有 8 張黑桃，整副牌中黑桃的總數為 $S = 13$。因此，剩下的黑桃數量為 $S - 8 = 5$。 ‖ ‖ step 2 ⋮ 西家有 13 張牌。我們需要找到這 13 張牌中恰好有一張黑桃的機率。 ‖ ‖ step 3 ⋮ 選擇 1 張黑桃的方式數量為 $ \binom{5}{1} = 5$。 ‖ ‖ step 4 ⋮ 選擇 12 張非黑桃的方式數量為 $ \binom{39}{12} = 15,817,620$。 ‖ ‖ step 5 ⋮ 選擇西家 13 張牌的總方式數量為 $ \binom{52}{13} = 635,013,559,600$。 ‖ ‖ step 6 ⋮ 因此，西家恰好有一張黑桃的機率為 $ \frac{\binom{5}{1} \cdot \binom{39}{12}}{\binom{52}{13}} = \frac{5 \cdot 15,817,620}{635,013,559,600} \approx 0.0654$。 ‖ ∻Answer∻ ⚹The probability that the West player has exactly one spade is approximately 0.0654.⚹ ∻Key Concept∻ ⚹Conditional Probability⚹ ∻Explanation∻ ⚹The problem involves calculating the probability of a specific event (West player having exactly one spade) given a certain condition (South and North players having 8 spades). This is done using combinatorial methods to count the favorable outcomes and the total possible outcomes.⚹◊What is the formula for calculating the probability of the West player having exactly one spade in their 13 cards?⍭ Generate me a similar question◊

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