Probability Ques 87
Passage Type Questions
Football teams $T _1$ and $T _2$ have to play two games against each other. It is assumed that the outcomes of the two games are independent. The probabilities of $T _1$ winning, drawing and losing a game against $T _2$ are $\frac{1}{2}, \frac{1}{6}$ and $\frac{1}{3}$, respectively. Each team gets $3$ points for a win, $1$ point for a draw and $0$ point for a loss in a game. Let $X$ and $Y$ denote the total points scored by teams $T _1$ and $T _2$, respectively, after two games.
(2016 Adv.)
$P(X>Y)$ is
(a) $\frac{1}{4}$
(b) $\frac{5}{12}$
(c) $\frac{1}{2}$
(d) $\frac{7}{12}$
Show Answer
Answer:
Correct Answer: 87.(b)
Solution:
Formula:
- Here, $P(X>Y)=P\left(T _1\right.$ win $) P\left(T _1\right.$ win $)$ $+P\left(T _1 \text { win }\right) P(\text { draw })+P(\text { draw }) P\left(T _1 \text { win }\right) $
$= (\frac{1}{2} \times \frac{1}{2})+ (\frac{1}{2} \times \frac{1}{6})+(\frac{1}{6} \times \frac{1}{2})=\frac{5}{12}$
BETA
