Two red balls and two white balls are placed in a bag Balls

Two red balls and two white balls are placed in a bag. Balls are drawn one by one, at random and without replacements. The random variable X is the number of white balls drawn before the first red ball is drawn.

a. Find the probability distribution of X.

b. Find E(X) and Var(X).

c. The sample mean for 80 independent observations of X is denoted by X . Using a suitable approximation, find P( X >0.75).

Solution