Question

Consider a standard 52-card deck. If you draw 25% cards from the deck without replacement.

What is the probability that your hand will contain one ace?

What is the probability that your hand will contain no ace?

Answer 1

25% of the cards means 13 cards are being drawn out.

a) Probability that the hand will contain one ace is computed here as:

= Number of ways to get one ace from 4 aces * Number of ways to select 12 cards from remaining 48 cards / Total number of ways to get 13 cards from 52 cards

Therefore 0.4388 is the required probability here.

b) Probability that there is no ace in the set of cards selected is computed here as:
= Number of ways to select 13 cards from the 48 non ace cards / Total number of ways to get 13 cards from 52 cards

Therefore 0.3038 is the required probability here.