Question

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 ___ 

Answer 1

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