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Question

# Three numbers are chosen at random without replacement from {1,2,...,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 =6.minimum probability =3.Let 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 be ′3′ and maximum probabilities is ′6′ then, we get.P(A∩B)=3,4,5,6So, in between we 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′ and maximum probabilities ′6′ no. of cases =2∴ the probabilities =Total no.of cases between ′3′ and ′6′Total no.of cases.Probabilities =210=15⇔P=15∴ correct option is C

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