If each element of a second order determinant is either zero or one, what is the probability that the value of determinant is positive? (Assume that the individual enteries of the determinant are chosen independently, each value being assumed with probability $1 half right parenthesis.$

Solution

There are four entries in determinant of 2 × 2 order. Each entry may be filled up in two ways with 0 or 1.
∴ number of determinants that can be formed = 2⁴ = 16
∴ total number of cases = 16
The value of determinant is positive in the cases
$open vertical bar table row 1 0 row 0 1 end table close vertical bar comma space open vertical bar table row 1 0 row 1 1 end table close vertical bar comma space open vertical bar table row 1 1 row 0 1 end table close vertical bar$
$therefore space space$ number of favourable cases = 3
$therefore$ the probability that the determinant is positive = $3 over 16.$

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Probability

If each element of a second order determinant is either zero or one, what is the probability that the value of determinant is positive? (Assume that the individual enteries of the determinant are chosen independently, each value being assumed with probability $1 half right parenthesis.$

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