Question

A natural number is selected at random from the set \( A=\{x: 1 \leq x \leq 50\} \). Find the probability such that the number satisfies the inequation \( x^{2}-13 x \leq 30 \).

Answer 1

x²−13x−30≤0
(x−15)(x+2)≤0
Since xϵ[1,50]
Hence x≤15
Therefore the values of x which satisfies the above inequality is [1,15]
Hence, first 15 natural numbers.
Therefore the required probability is 15/50

= 3/10