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A determinant is chosen at random from t...

A determinant is chosen at random from the set of all determinant of order 2 with elements 0 or 1 only. Find the probability that the determinant chosen is nonzero.

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Determinant `Delta` of order 2 will be of the form `|(a, b),(c,d)|`.
`therefore Delta = ad - bc`
The total number of ways of choosing a, b, c and d is
`2 xx 2 xx 2 xx 2 = 16`
Now, `Delta ne 0` if and only if either ad = 1, bc = 0 or ad = 0, bc = 1.
For ad = 1, (a,d) -= (1, 1).
For bc = 0, (b, c) -= (0, 1), (1, 0), (0, 0).
So, three cases are there.
Similarly, for ad = 0 and bc = 1, there will be three cases.
`therefore` Number of favourable cases = 3 + 3 = 6
So, required probability = `(6)/(16) = (3)/(8)`
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