## Question

A natural number *x* is chosen at random from the first one hundred natural numbers. The probability that is

### Solution

7/25

Sign of *E* is same as that of sign of

(*x* – 20) (*x* – 30) (*x* – 40) = *F*(say).

Note that *F* < 0 if and only if

0 < *x* < 20 or 30 < *x* < 40.

∴ *E* < 0 in (0, 20) ∪ (30, 40)

Thus, *E* is negative for *x* = 1, 2,….,19, 31, 32,….,39, that is *E*, < 0 for 28 nature numbers.

∴ Required probability = 28/100 = 7/25.

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