Question

Compute probability of randomly selected 5 cards from deck of 52 cards and getting only one Jack.

Answer 1

5/25

Explanation:

Probability would be that you randomly select 5 cards so the selection goes above the fraction and the total amout of cards goes below.

Answer 2

3243 / 10829 ≈ 0.2995

Explanation:

There are 52 cards in a deck. 5 cards are selected, so the number of possible combinations is ₅₂C₅.

Of the 5 cards selected, 1 is a Jack and 4 are non-Jacks.

There are 4 Jacks in a deck. The number of ways of choosing 1 Jack from 4 is ₄C₁.

There are 48 non-Jacks in a deck. The number of ways of choosing 4 non-Jacks from 48 is ₄₈C₄.

So the probability is:

P = ₄C₁ ₄₈C₄ / ₅₂C₅

P = 4 × 194580 / 2598960

P = 778320 / 2598960

P = 3243 / 10829

P ≈ 0.2995