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Question
Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain at least one ace?
Solution
Let S denote the sample space.
Then n(S) = 52
Thus, five cards can be drawn in 52C5 ways.
∴ Total number of elementary events = 52C5
Probability for at least one ace = 1 – Probability (no ace)
= \[1 - \frac{^{48}{}{C}_5}{^{52}{}{C}_5}\]
= \[1 - \frac{35673}{54145} = \frac{18472}{54145}\]
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