Question 2.8: Consider a well-shuffled deck of 52 cards (Example 28 in Cha......
Consider a well-shuffled deck of 52 cards (Example 28 in Chapter 1), and suppose we draw at random three cards. What is the probability that at least one is an ace?
Let A be the required event, and let A_i be defined by: A_i = “exactly i cards are aces,” i = 0, 1, 2, 3. Then, clearly, P(A)=P(A_{1}\cup A_{2}\cup A_{3}). Instead, we may choose to calculate P(A) through P(A^{c})=1-P(A_{0}), where
P(A_{0})={\frac{\binom{48}{3} }{\binom{52}{3} }}={\frac{48\times47\times46}{52\times51\times50}}={\frac{4,324}{5,525}},\quad{\mathrm{so~that}}\,P(A)={\frac{1,201}{5,525}}\simeq0.217.Related Answered Questions
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