A box of candy hearts contains 52 hearts of which 19 are whi

A box of candy hearts contains 52 hearts of which 19 are white, 10are tan, 7 are pink, 3 are purple, 5 are yellow, 2 are orange, and6 are green. If you select 9 pieces of candy randomly from the box,without replacement, give the probability that

a) no more than three of the hearts are white

Solution

From the 52 candy 19 are white, so the probability of getting a white candy is 19/52

now, Let X be the random variable denoting the number of white candy in 9 sample where each white candy has probability is 19/52

so , X~Bin(9, 19/52)

to find

P(X<=3)=P(X=0)+P(X=1)+P(X=2)+P(X=3)

By calculation we get P(X<=3)=0.570