Probability

Question

We choose 10 random cards from a normal deck of cards(52 cards). What is the probability that we get:
a. 0 aces
b. maximum 3 aces
c. at least 1 ace and at least one face card

Answer 1

a.  P(0 aces in 10 cards drawn WITHOUT REPLACEMENT) = ₄₈C₁₀ ÷ ₅₂C₁₀  because you'd have to choose ten cards from the 48 non-aces.

 

b. Do this as the sum of these probabilities: P(no aces) +  P(one ace) + P(2 aces) +P(3 aces). To help you get started:

 

    P(1 ace) is ₄C_1•48C_{9 ÷ 52}C_10.