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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))` |
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Answer» Correct Answer - 0.5 `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)` |
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