Homework SourseSuppose you draw 5 cards out of a deck of 52 and get 2 spade
Suppose you draw 5 cards out of a deck of 52 and get 2 spades and 3 hearts. What is the probability that the first card drawn was a spade?
Suppose you draw 5 cards out of a deck of 52 and get 2 spades and 3 hearts. What is the probability that the first card drawn was a spade?
Suppose you draw 5 cards out of a deck of 52 and get 2 spades and 3 hearts. What is the probability that the first card drawn was a spade?
Solution
2 of the 5 cards are spades. Thus, the probability that any of the cards selected is a spade is simply 2/5. Note - the probability can also be worked out in a much more difficult manner. P(2 spades and 3 hearts selected) = C(13,2)C(13,3)/C(52,5) P(first card is a spade and then 1 spade and 3 hearts) = 1/4 * C(12,1)C(13,3)/C(51,4) Then, 1/4 * C(12,1)C(13,3)/C(51,4)/(C(13,2)C(13,3)/C(52,5)) = 1/4*52/5*C(12,1)/C(13,2) = 1/4*52/5*12/(13*12/2) = 13/5/(13/2) = 2/5
