Let S be the sample space of all 3 × 3 matrices with entries from the set {0, 1}.

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Let S be the sample space of all 3 × 3 matrices with entries from the set {0, 1}. Let the events E1 and E2 be given by

E1 = {A ∈ S : det A = 0} and

E2 = {A ∈ S : sum of entries of A is 7}.

If a matrix is chosen at random from S, then the conditional probability P(E1|E2) equals ___

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For sum 7 we need seven 1s and two zeroes

Number of different possible matrices = 9! /7!2! = 36 = n(E2

For |A| = 0 both zeroes must be in same row/column

Number of matrices such that their determinant is