Probability
Geometric probability, continuous sample space
nta_pyq_2023_jan
Grade 12
Question:
Let A be the event that the absolute difference between two randomly chosen real numbers in the sample space $[0, 60]$ is less than or equal to $a$. If $P(A) = \frac{11}{36}$, then $a$ is equal to ___.
Step-by-Step Solution
Key Concept: Use geometric probability: $P(|x-y| \leq a) = 1 - (60-a)^2/60^2$
$P(A) = \frac{60^2 - (60-a)^2}{60^2} = \frac{11}{36}$. $\frac{(60-a)^2}{3600} = \frac{25}{36} \Rightarrow (60-a)^2 = 2500 \Rightarrow 60-a = 50 \Rightarrow a = 10$. Answer: 10
Correct Answer: 10