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Question

Three numbers are chosen at random without replacement from {1,2,3,….,8}. The probability that their minimum is 3, given that their maximum is 6, is :

A
25
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B
38
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C
15
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D
14
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Solution

The correct option is C 15Three numbers are chosen at random without replacement from 1,2,...8maximum probability =6minimum probability =3Let us consider two events A and B as given two probabilities.So we get P(A∩B) So, as per given data minimum probabilities. Should ′3′ and maximum probabilities is ′6′ then,we getP(A∩B)=3,4,5,6So, now we have may get two probabilities which are less than ′6′So now we have two cases.We get nCr=5C2 [′5′ because given there is no replacement]5C2⇒5×42=202=10.∴ total no of classes =10 for minimum probabilities ′3′ maximum probabilities ′6′ no. of cases =2∴ the probabilities =Total no. of cases between ′3′ and ′6′Total no. of casesProbabilities =210=15⇔P=15

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