Probability
Probability
nta_abhyas_2025
Grade 12
Question:
A number $x$ is chosen at random from the set $\{1, 2, 3, \ldots, 100\}$. Define the event $A$ = the chosen number $x$ satisfies $\frac{(x-10)(x-50)}{x-30} \le 0$, then $P(A)$ is
$0.20$
$0.51$
$0.71$
$0.70$
Step-by-Step Solution
Key Concept: Solve the quadratic equation by factoring to find the valid probability value
We need to find the value of $p$ from the given equation. Starting with $5p - 5p^2 = 2 - 2 - 3p^2 + 4p$, we simplify to get $3p^2 - p = 0$, which factors as $p(3p - 1) = 0$. This gives us $p = 0$ or $p = \frac{1}{3}$. Since we need $p \neq 0$, we have $p = \frac{1}{3}$. Therefore $9p = 3$.
Correct Answer: C