There are three similar boxes containing i). 6 black and 4 white balls. ii). 3 black and 7 white balls. iii). 5 black and 5 white balls, respectively. If you choose one of the three boxes at random and from that particular box pick up a ball at random and find that to be black, what is the probability that the ball was picked up from the second box ?
Answer: A Black - Box-1 (6), Box-2 (3), Box-3 (5) White - Box-1 (4), Box-2 (7), Box-3 (5) each box is equally likely to be selected after that each balls is equally likely to be selected. All balls have same probability to be selected. Hence, required probability = 3/(6+4+5) = 3/14
Q. No. 26:
There are three events A, B and C, one of which must and only can happen. If the odds are 8:3 against A, 5:2 against B, the odds against C must be :
Answer: C According to the question, P(A')/P(A) = 8/3 , P(A) = 3/11 and P(A') = 8/11 Also, P(B')/P(B) = 5/2 => P(B) = 2/7 and P(B') = 5/7 Now, out of A,B and C, one and only one can happen. P(A)+P(B)+P(C) = 1 P(C) = 34/77 P(C') = 1- P(C) = 43/77 So odd against C = P(C)/P(C') = 43/34 = 43:34
Q. No. 27:
The game of 'Chunk-a-luck' is played at carnivals in some parts of Europe. Its rule are as follows : If you pick a number from 1 to 6 and the operator rolls three dice. If the number you picked comes up on all three dice, the operator pays you Rs 3. If it comes up on two dice, you are paid Rs 2 and if it comes up on just one die, you are paid Rs 1. Only if the number you picked does not comes at all, you pay the operator Rs 1. The probability that you will win money playing in this game is :
Answer: C We know that the probability that a particular number will come on a dice is 1/6 and the probability that a particular number will not come on a dices is 5/6. Now, in the question there are 3 dices. So, probability that picked number will not come in any of 3 dice = (5/6)3 . And, we know that we will lose in only this condition that our picked number will not come on any three dices. Probability of losing = (5/6)3 = 0.58 Probability of winning = 1- 0.58 = 0.42.