Probability
Probability
nta_abhyas_2025
Grade 12
Question:
If $\frac{1-p}{p}, \frac{1-q}{q}$ and $\frac{1-r}{r}$ are probabilities of mutually exclusive events of a random experiment, then the range of $p$ is
\frac{1}{3} \le p \le \frac{1}{2}
\frac{1}{2} \le p \le \frac{2}{3}
\frac{1}{3} \le p \le \frac{2}{3}
\frac{1}{3} \le p \le \frac{5}{8}
Step-by-Step Solution
Key Concept: Counting favorable outcomes from given constraints and dividing by total possible outcomes
Given constraints yield favorable case = 60 and total case = $^{120}C_2$. The required probability is $\frac{60}{^{120}C_2} = \frac{60}{\frac{120 \times 119}{2}} = \frac{60}{7140} = \frac{1}{119}$. Therefore $100k = 4$.
Correct Answer: 4