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Question

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 is non-zero is

A
316
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B
38
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C
58
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D
78
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Solution

The correct option is A 38
P (determinant is non zero) = 1-P(determinant is zero)
[abcd]
total no. of elements in determinant of order 2=4
And each element can have value either 0 or 1
Hence, total no. of determinants possible = 16
Determinant is zero only when ad=bc
Case1: a=b=c=d=1 , determinants = 1
Case2: either of a, d and b,c is zero, no. of determinants possible =4
case3: three of a,b,c,d are zero, no. of determinants possible =4
case4 : a=b=c=d = 0 , determinants =1
P = 1 - 10/16=3/8

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