Question

A box contains 5 blue, 10 green, and 5 red chips. We draw 4 chips at random and without replacement. If exactly one of them is blue, what is the probability mass function of the number of green balls drawn?

Answer 1

Total number of chips; 5+10+5 = 20

It is given that out of 4 draws one is blue so number of chips remaining is 20-1 = 19 out of which 5-1 = 4 are blue and 10 are green.

Let X is a random variable shows the number of green chips out of remaining 3. So here X will have hyper geometric distribution with parameters as follow:

Population size: N = 19

Sample size: n=3

Number of successes in population: k = 10

The probability mass function of X is

Following table shows the pmf:

X	P(X=x)
0	0.086687307
1	0.371517028
2	0.417956656
3	0.123839009