A Determinant Is Chosen At Random From The Set Of All Determinants Of Order 2 With Elements 0 Or 1 only. The Probability That The Determinant Chosen Is Non – Zero Is

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A determinant is chosen at random from the set of all determinants of order 2 with elements 0 or 1 only. The probability that the determinant chosen is non – zero is


Correct option is


A determinant of order 2 is of the from


It is equal to ad – bc. The total number of ways of choosing abc and dis 2 × 2 × 2 × 2 = 16. Now ∆ ≠ 0 if and only y if either ad = I, bc = 0 orad = 0, bc = 1. But ad = 1, bc = 0 if and only if a = d = 1. And at least one of bc is zero. Thus ad = 1, bc = 0 in three cases. Similarly, ad = 0,bc = 1 in three cases. Thus, the probability of the required event is 6/16 = 3/8.



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