Question

An urn contains 3 red and 2 white marbles. Two marbles are drawn one by one with replacement from the urn. Find the probability distribution of the number of white balls. Also, find the mean of the number of white balls drawn. 

Answer 1

Consider, p =Probability of getting a white marble = `2/5`

and q = Probability of getting a red marble = `3/5`

Let X denotes the number of red balls in two draws.

Now, P(X = 0) = P (no white marble) = P (all red marble)

= `3/5 xx 3/5 = 9/25`

P(X = 1) = P (one white marble and one red marble).

= `2/5 xx 3/5 + 3/5 xx 2/5 = 12/25`

P(X = 2) = P (two white marbles)

= `2/5 xx 2/5 = 4/25`

Hence, the probability distribution is shown below.

X	0	1	2
P(X)	`9/25`	`12/25`	`4/25`

Now, mean of distribution,

E(X) = ∑X · P(X)

= `0 xx 9/25 + 1 xx 12/25 + 2 xx 4/25`

= `0 + 12/25 + 8/25`

= `20/25`

= `4/5`