Question

Five cards are drawn from a pack of 52 cards. What is the chance that these 5 will contain at least one ace?

 

Answer 1

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)
                                                  = \[1 - \frac{^{48}{}{C}_5}{^{52}{}{C}_5}\]

                                                 = \[1 - \frac{35673}{54145} = \frac{18472}{54145}\]