JEE PYQ: Probability Question 8
Question 8 - 2021 (24 Feb Shift 1)
Let $B_i$ ($i = 1, 2, 3$) be three independent events in a sample space. The probability that only $B_1$ occur is $\alpha$, only $B_2$ occurs is $\beta$ and only $B_3$ occurs is $\gamma$. Let $p$ be the probability that none of the events $B_i$ occurs and these 4 probabilities satisfy the equations $(\alpha - 2\beta)p = \alpha\beta$ and $(\beta - 3\gamma)p = 2\beta\gamma$. All the given probabilities are assumed to lie in the interval $(0,1)$. Then $\frac{P(B_1)}{P(B_3)}$ is equal to ______.
Show Answer
Answer: 6
Solution
Same structure as Q4. Let $x, y, z$ be probabilities. $\alpha = x(1-y)(1-z)$, etc. From equations: $x = 2y$ and $y = 3z$. So $\frac{x}{z} = 6$.
BETA
