## 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 chosen is non – zero is

### Solution

3/8

A determinant of order 2 is of the from

It is equal to *ad* – *bc*. The total number of ways of choosing *a*, *b*, *c* and *d*is 2 × 2 × 2 × 2 = 16. Now âˆ† ≠ 0 if and only *y* if either *ad* = I, *bc* = 0 or*ad* = 0, *bc* = 1. But *ad* = 1, *bc* = 0 if and only if *a* = *d* = 1. And at least one of *b*, *c* is zero. Thus *ad* = 1, *bc* = 0 in three cases. Similarly, *ad* = 0,*bc* = 1 in three cases. Thus, the probability of the required event is 6/16 = 3/8.

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