Let S be the sample space of all 3 × 3 matrices with entries from the set 0 , 1 . Let the events E 1 and E 2 be given by E 1 = A ∈ S :   d e t   A = 0 and E 2 = A ∈ S : sum of entries of A is 7 . If a matrix is chosen at random from S , then the conditional probability P E 1 E 2 equals____

Step-by-step solution

For sum to be seven, we need seven 1 s and two 0 s Number of different possible matrices= = 9 7   2 = 36 Eg. 1 1 1 1 1 1 0 0 1 arrangement of seven 1 s and two 0 s Now, for determined of matrix to be zero, both the zero must be in same row or in same column. Eg. 1 0 0 1 1 1 1 1 1 Now, arrangement of 0s and 1 s = 6 S e l e c t i o n   o f a   c o l u m n / r o w   ×    3 a r r a n g e m e n t o f   t w o   0 s a n d   o n e   1   i n   a &#