A box contains 4 red and 3 blue balls A person chooses one a

A box contains 4 red and 3 blue balls. A person chooses one at a time without replacement until he gets a red ball. The he stops. X is the number of balls he chooses.

a) Make a tree diagram for this experiment.

b) Write the distribution of X.    c) Find E(X) and (X).

Solution

a) there are 4 red and 3 blue balls.

one is choosen till we get red

diagram or cases:

1) when we get red at 1st chance

probability = 4/7

2) when we get 1st blue and 2nd red

probability = 3/7*4/6 = 2/7

3) when we get 2 times blue and 3rd red

probability = 3/7*2/6*4/5 = 4/35

4) when we get 3 blue and 4th red

probability = 3/7*2/6*1/5*4/4 = 1/35

b) probability given in above part is the distribution of x

c)E(X) = X1*P(X1)+X2*P(X2)

= 3*3/7+4*4/7

= 25/7

SIMILARLY WE CAN FIND THE VARIANCE.