1. You have three boxes that contains certain number of blue and red balls. Firs

Question

1. You have three boxes that contains certain number of blue and red balls. First box has 2 red balls, 10 blue balls; second box has 4 red balls and 8 blue balls; third box has 9 red balls and 3 blue balls. You roll a fair die and if the face on top is 1 or 2 you pick a ball from the first box; 3 or 4 you pick a ball from the second box; and 5 or 6 you pick a ball from the third box. Based on this random experiment answer the following questions. (a) What is the probability that the ball you pick is red ? (b) If the ball you picked is red, then what is the probability that the outcome for the roll of the die is 3? Ca 38

Explanation / Answer

Question 3(a)

Here,

Pr(1 or 2 in rolling a die) = Pr(3 or 4 in rolling a die) = Pr(5 or 6 in rolling a die) = 1/3

Pr(Red l Box 1) = 2/12 = 1/6

Pr(Red l Box 2) = 4/12 = 1/3

Pr(Red l Box 3) = 9/12 = 3/4

Pr(Ball is red) = 1/6 * 1/3 + 1/3 * 1/3 + 3/4 * 1/3 = 5/12

(b) Now the ball drawn is red so

Pr(Outcome of the die would be 3 l Red) = Pr(OUtcome of the die would be 3 )/ Pr(Red) = (1/2 * 1/3 * 1/3)/ (5/12) = 2/15

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