Let S be the set of matrices of order `3xx3` such that all elemtns of the matrix belong to `{0,1}`
let `E_(1)={A in S:|A|=0}` where |A| denotes determinant of matrix A
`E_(2)={A in S:` sum of elements of `A=7`} find `P(E_(1)//E_(2))`

Options

A. `0.1`
B. `0.9`
C. `1.2`
D. `0.5`

Answer

D

Explanation

`E_(2)`: sum of elements of `A=7implies `These are 7 ones and 2 zeros
Number of such matrices `= .^(9)C_(2)=36`
Out of all such matrices `E_(1)` eill be those when both zeros lie in te same row or in te same colume
eg. `[{:(1,1,1),(0,1,1),(0,1,1):}]`
`n(E_(1)capE_(2))=2xx underset(uarr)(.^(3)C_(2))xx underset(uarr)(.^(3)C_(2)=18)`
so `n(E1//E2)=(n(E_(1)capE_(2)))/(n(E_(2)))=(18)/(36)=(1)/(2)`