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Question

A second order determinant is written randomly using the numbers 1 and −1as its elements, the probability that the value of the determinant is non zero is

A
13
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B
23
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C
38
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D
12
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Solution

The correct option is D 12
n(S)= sample space =24=16
(there are four places to fill with 1 and -1 i.e., every
place can be filled by 2 ways).
n(A)= Number of determinants whose value is zero
n(A)= It can be happened if all entry are +ve = 1 case only
only two entries are negative 4C2=6 case
all four entries are negative =4C2=1case
n(A)=8 like cases
(1111)onecase,(1111)onecase,(1111)6case so on.
P(A)=n(A)n(S)=816=12

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