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Surya Dhanraj
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in Probability
Sep 17, 2017

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Best answer

This question is based on conditional probability..

We know :

P(A | B) = P(A ∩ B) / P(B)

So here P(B) = P(maximum of 3 numbers = 6)

So we have 5 numbers to chosse from to choose remaining 2 numbers which can be done in ^{5}C_{2} = 10 ways..

Hence P(B) = 10 / ^{8}C_{3}

Now coming to P(A ∩ B) , it suggests minimum of 3 numbers should be 3 and maximum should be 6..

So only possibility is to choose the middle number which can be 4 or 5 and hence 2 ways.

Hence P(A | B) = ( 2/^{8}C_{3} ) / (10 / ^{8}C_{3})

= 2 / 10 = 1 / 5

**Hence required conditional probability = 1 / 5**