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in Introduction to Probability Theory by (47.8k points)
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A matrix is chosen at random from a set of all matrices of order 2, with elements 0 or 1 only. The probability that the determinant of the matrix chosen is not zero will be

(a) 3/16

(b) 3/8

(c) 1/4

(d) 5/8

1 Answer

+1 vote
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Best answer

(b) 3/8

Then given elements are 0 and So each term of a matrix can be filled (Using or 1) is 2 ways. 

The No. of elements is a 2 × 2 matrix = 2 × 2 = 4. So the possible ways of filling the elements of a 2 × 2 matrix is 24 = 16 (i.e.,) n(S) = 16 

Let A be the event of getting a 2 × 2 matrix for which the determinant value is non zero.

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