Question-35 A number x is chosen at random from the set {1,2,3,4 \ldots \ldots, 100}. Define the event : A such that the chosen number x satisfies \frac{(x-10)(x-50)}{(x-30)} \geq 0. Then P(A) is
A) 0.51
B) 0.70
C) 0.71
D) 0.20
Answer: C) 0.71
Explanation
Given \frac{(x-10)(x-50)}{(x-30)} \geq 0
Let x \geq 10, x \geq 50 equation will be true \forall x \geq 50
as \left(\frac{x-50}{x-30}\right) \geq 0, \forall x \in[10,30)
\frac{(x-10)(x-50)}{x-30} \geq 0 \forall x \in[10,30)Total value of \boldsymbol{x} between \mathbf{1 0} to \mathbf{3 0} is \mathbf{2 0}.
Total values of x between \mathbf{5 0} to \mathbf{1 0 0} including \mathbf{5 0} and \mathbf{1 0 0} is \mathbf{5 1}
Total values of x=51+20=71
P(\mathrm{~A})=\frac{71}{100}=0.71