18 Suppose that there are 8 ping pong balls in a bucket Thre

18. Suppose that there are 8 ping pong balls in a bucket. Three of the ping pong balls are white, and 5 of the ping pong balls are red. The experiment is set up where you select one ball, record its color and set it aside. You then select a second ball and record its color. a. Draw and label a tree diagram. b. What are all of the possible outcomes and their probabilities?

Solution

3W+ 5R

1^st draw: W or   R

2^nd draw: W or R

The possible cases are (W1, W2),(W1, R2) , (R1,W2) , (R1, R2)

Here : W1 means drawing white ball in the first draw

R2= drawing red ball in the second draw. Similar interpretation for others.

(W1, W2): 3/8 * 2/7=0.1071

(W1, R2) : 3/8*5/7 = 0.2678

(R1,W2): 5/8* 2/7= 0.1785

(R1,R2)= 5/8*4/7= 0.3571