Question

Suppose that colored balls are distributed in 3 boxes as follows: box 1 contains 2 red, 3 white and 5 blue balls, box 2 contains 4 red, 1 white and 3 blue balls, and box 3 contains 3 red, 4 white and 5 blue balls. A box is selected at random, one ball is chosen from it and it is observed to be red. What is the probability that box 3 was selected

Answer 1

possible event 1
te. 3
ans is 1/3

Answer 2

The probability that the box 3 was selected is 1 / 10.

• Number of balls of each color in box 1 :

Red = 2, White = 3,  Blue = 5

Therefore, total number of balls in box 1 = 2 + 3 + 5 = 10

• Number of balls of each color in box 2 :

Red = 4,  White = 1,  Blue = 3

Therefore, total number of balls in box 2 = 4 + 1 + 3 = 8

• Number of balls of each color in box 3 :

Red = 3, White = 4,  Blue = 5

Therefore, total number of balls in box 3 = 3 + 4 + 5 = 12

• Now, probability that box 3 was chosen = Number or red balls in box 3 / Total number of all balls in all the boxes.

• Total number of balls in all the boxes =  10 + 8 + 12 = 30

• Therefore, probability that the red ball was drawn from box 3 = 3 / 30 = 1 / 10 .