You get dealt 6 cards from a deck A is the event that you ge

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 6 cards include 4 queens. Find P(A), P(B), P(A union B), P(A intersect B), and P(A|B).

Solution

p(A)=(13c2*13c1*13c1*13c2)/52c6 =0.0505

p(B)=(4c4*48c2)/52c6=5.54*10^-5

p(A intersection B)=p(A)*p(B)=2.798*10^-6

p(A union B)=p(A)+p(B)-p(A intersection B)=0.0505 (appx)

p(A|B)=p(A intersection B)/p(B)=0.0505 (appx)