Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 11

# Five Cards Are Drawn from a Pack of 52 Cards. What is the Chance that These 5 Will Contain: (Ii) at Least One Ace? - Mathematics

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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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 33 Probability
Exercise 33.3 | Q 17.2 | Page 46