Question

PLEASE PROVIDE FORMULAS USED IN THIS QUESTION

3. (6 points) Two marbles are drawn at random with replacement from a box containing 2 red, 3 green, and 4 blue marbles. Let's define the following events: A= {two red marbles are drawn}, B = {two green marbles are drawn), C = {two blue marbles are drawn}, D= {two marbles of the same color are drawn} Find each of the following probabilities: P(A), P(B), P(C), P(D), and P(A|D). -1-

Answer 1

since experiment is done with replacement , therefore events are independent and sample size =2+3+4=9 remains fixed from trail to trail.

P(A)=P(two red marbles) =P(first is red and 2nd is red)=P(first red)*P(2nd red)=(2/9)*(2/9)=4/81

P(B) =P(two green marbles) =(3/9)*(3/9)=1/9

P(C) =P(two blue marbles) =(4/9)*(4/9)=16/81

P(D) =P(A)+P(B)+P(C) =4/81+1/9+16/81 =29/81