An 8-sided die is rolled and depending on the result a ball is then chosen from

Question

An 8-sided die is rolled and depending on the result a ball is then chosen from one of three boxes. If the roll results in a 1 a ball is drawn from box A, if the roll results in a 2, 3, or 4 a ball is drawn from box B, and if the roll results in a 5, 6, 7, or 8 a ball is drawn from box C. If box A contains 5 red, 8 white, and 2 black balls, box B contains 8 red and 7 black balls, and box C contains 5 white and 10 black balls:

a) What is the probability that you draw a red ball?

b) What is the probability that you draw a black ball that does not come from box B?

c) What is the probability that you drew a ball from box A given that the ball is white?

d) What is the probability that you draw a black ball given that you drew the ball from box C?

Explanation / Answer

a) The red ball come from either any one of the boxes A, B and C

Box A:

If we choose Box A then P(A) = 1/8          Apear 1 on die when it is throwing

P(getting red ball from Box A) = 5 / 15

P(getting red ball when Choose Box A is) = (1/8)*(5/15) = 5 / 120

Box B:

If we choose Box A then P(A) = 3/8          Apear 2,3,4 on die when it is throwing

P(getting red ball from Box A) =8 / 15

P(getting red ball when Choose Box A is) = (3/8)*(8/15) = 24 / 120

Box c: There is no red ball in Box C

The probability that you draw a red ball is 5/120 + 24/120 = 29/120

b) the probability that you draw a black ball that does not come from box B is

                                     =    P(draw black ball from Box A or Box C)

                                      = P(Drawn black ball from Box A) + P(Drawn black ball from Box C)

                                      = (1/8) (2/15)   +   (4/8)(10/15) = 42/120

c) P(draw a ball from box A / the ball is white) = P(Draw a ball from Box A and the ball is white) / P(Ball is white)

                                                                        = (1/8 * 8/15) / (1/8 * 8/15   +   4/8 * 5/10)

                                                                         = (8/120) / (28/120) = 8/28

d) P(you draw a black ball / that you drew the ball from box C) is

                      = P(a black ball from box C) / P(ball from Box C)

                      = (4/8 * 10/15) / (4/8) = 10/15

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