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