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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 15
Three numbers are chosen at random without replacement from 1,2,...8
maximum probability =6
minimum probability =3
Let us consider two events A and B as given two probabilities.
So we get P(AB)
So, as per given data minimum probabilities. Should 3 and maximum probabilities is 6 then,
we get
P(AB)=3,4,5,6
So, 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]
5C25×42=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 6Total no. of cases
Probabilities =210=15P=15

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