In the game of bridge four players are dealt 13 card hands f

In the game of bridge, four players are dealt 13 card hands from a standard deck of cards. For both of the following, carefully define a relevant sample space and show all probability calculations. Find the probability that you are dealt three clubs. Find the probability that you are dealt three clubs, and the player sitting across from you is dealt the other 10 clubs.

Solution

a) prob that you are dealt 3 clubs = 13C3 * 39C10 / 52C13 = 0.2863

b) prob = (13C3 * 39C10 * 10C10 * 29C3 )/ (52C13 * 39C13) = 1.288 * 10^-7