There are three boxes with balls The first box is yellow the

There are three boxes with balls. The first box is yellow, the second box is green, and the third box is white. Thre are 7 red and 12 blue balls in the yellow box, 3 red and 6 blue balls in the green box, and 11 red and 6 blue balls in the white box. First a box is selected at random, and then from the selected box a ball is selected at random.

(a) If selected box is tellow find the probability that the selected ball is blue.

(b) If selected ball is red find the probability that it was selected from the yellow box.

(c) If selected ball is blue find the probability that it was selected from the white box.

Solution

a)Probability that if the selected box is yellow and the selected ball is blue:

12/19

b)p()

(1/3*7/19)/(1/3*7/19+1/3*3/9+1/3*11/17)

=0.122/(0.122+0.111+0.215)

=0.122/0.448=0.27

c)

(1/3*6/17)/(1/3*12/19+1/3*6/9+1/3*6/17)

=0.117/(0.21+0.22+0.117)

=0.117/0.547=0.21