InterviewSolution
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InterviewSolution
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Let S be the sample space of all 3xx3 matrices with entries from the set {0,1} . Let the events E_1 and E_2 be given by E_1={A in S: det A=0} and E_2={A in 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........... |
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Answer» `E_1={A in S :det(A)=0}` and `E_2={A in S: "Sum of entries of" A is 7}`. For event `F_2`. Means sum of entries of matrix A is 7, then we need SEVEN 1s and two 0s. `therefore` Number of different possible matrices `=(91)/(7! 2!)rArr n(E_2)=36` For event `E_1,|A|=0`, both the zeroes must be in same row/column. `therefore` Number of matrices such that their determinant is zero. ` 6xx (3!)/(2!)=18=n(E_1 cap E_2)` `therefore` Requried probability, `P(E_1)/(E_2)=(n(E_1cap E_2))/(n(E_2))` ` = (18)/(36) =(1)/(2)=0.50`. |
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