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

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 PE1E2 equals____

Solution

For sum to be seven, we need seven 1s and two 0s
Number of different possible matrices= =97 2=36
Eg. 111111001 {arrangement of seven 1s and two 0s }
Now, for determined of matrix to be zero, both the zero must be in same row or in same column.
Eg. 100111111 Now, arrangement of 0s and 1s=6Selection ofa column/row ×  3arrangementof two 0sand one 1 in a row/column  =  18
Hence, required probability =1836=12
(Note: If two zero's lies on different row/column then 011101111=+1≠0 )

Asked in: JEE Advanced 2019 (Paper 1)

Practice more Probability questions on Aicharya