Leave answers in terms of symbols You get dealt 6 cards from

Leave answers in terms of symbols. You get dealt 6 cards from a deck. A is the event that you get exactly 2 spades, 1 heart, 1 diamond and 2 clubs in your six cards, B is the event that your 5 cards include 4 queens. Find (A), P(B), P(A?B) and P(A|B).

Solution

total size of sample space = 52C6 = 20358520

since there are 52 cards in a standard deck

total number of combinations satisfying event A

= 13C2 * 13C1 * 13C1 * 13C2 = 1028196

total number of combinations satisfying event B

= 4C4 * 48C2 = 1128

so,

P(A) = 1028196/20358520 = 0.05

P(B) = 1128/20358520 = 5.54 * 10^-5