SOLUTION: three yam tubers are chosen at random from 15 tubers of which 5 are spoilt. find the probability that; (a) none is spoilt (b) all are spoilt (c) exactly one is spoilt (d) at l

Algebra ->  Probability-and-statistics -> SOLUTION: three yam tubers are chosen at random from 15 tubers of which 5 are spoilt. find the probability that; (a) none is spoilt (b) all are spoilt (c) exactly one is spoilt (d) at l      Log On


   

Question 1162571: three yam tubers are chosen at random from 15 tubers of which 5 are spoilt. find the probability that;
(a) none is spoilt
(b) all are spoilt
(c) exactly one is spoilt
(d) at least one is spoilt

Answer by ikleyn(53751) About Me  (Show Source):
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(a)  It means that you chose all 3 yam tubers from the set of 15-5 = 10 yam tubers that are not spoilt.


     Therefore, the probability (a) is  P = %2810%2F15%29%2A%289%2F14%29%2A%288%2F13%29 = %282%2F3%29%2A%289%2F14%29%2A%288%2F13%29 = %283%2F7%29%2A%288%2F13%29 = 24%2F91 = 0.2637.         ANSWER




(b)  It means that you chose all 3 yam tubers from the set of 5 yam tubers that are spoilt.


     Therefore, the probability (b) is  P = %285%2F15%29%2A%284%2F14%29%2A%283%2F13%29 = %281%2F3%29%2A%282%2F7%29%2A%283%2F13%29 = %282%2F7%29%2A%281%2F13%29 = 2%2F91 = 0.0220.      ANSWER




(c)  In this case, the probability is  P = 3%2A%285%2F15%29%2A%2810%2F14%29%2A%289%2F13%29 = %285%2F7%29%2A%289%2F13%29 = 45%2F91 0.4945.      ANSWER




(d)  In this case, the probability is the COMPLEMENT to case (a)  P = 1 - 0.2637 = 0.7363.      ANSWER

Solved.