Box 1 contains 10 white and 12 black balls. Box Il contains 8 white and 10 black

Question

Box 1 contains 10 white and 12 black balls. Box Il contains 8 white and 10 black balls. Box Ill contains 11 white and 13 black balls. (a) A all is drawn at random from box l. find the probability that the ball is black. A box (I)-(lll) is selected by rolling one fair die. If the die shows {1} the box 1 is selected. If the die shows {2 or 3} the box ll is selected, otherwise box lll s selected. After the box is selected then a ball is drawn at random from the selected box. (b) Find the probability that the ball is White; A box (l)-(Ill) is selected with the same method as described above. A ball is drawn at random from the selected box is found to be white. (c) Find the probability that box (ll) was selected. (d) Find the probability that the ball did not come from box Ill.

Explanation / Answer

a) Probability of black ball from box1 = 12/22 =   0.5454
   Probaility of box selection = 3/6 = 1/2 = 0.5
   Probability of black ball when any box is randomly selected: 0.5 * (12/22) + 0.5 * (10/18) + 0.5 * (13/24)
                                                               :0.5 * 0.5454 + 0.5 * 0.5555 + 0.5 * 0.5416
                                                               : 0.8215
b) Probaility of box selection = 3/6 = 1/2 = 0.5
   Probability of white ball when any box is randomly selected: 0.5 * (10/22) + 0.5 * (8/18) + 0.5 * (11/24)
                                                               :0.5 * 0.4545 + 0.5 * 0.4444 + 0.5 * 0.4583
                                                               : 0.6786
c)Probability that box 2 is selected = 1/6 = 0.1666
Probability that ball did not come from box 3         : 1-1/6 = 0.8334

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