Paragraph: 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.…

Question

Paragraph: 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. Question: $P(X>Y)$ is

Aicharya · Accepted Answer

P X &#62; Y = P T 1 &#160; w i n &#160; P T 1 w i n + P T 1 w i n &#160; P m a t c h &#160; d r a w + P m a t c h &#160; d r a w . &#160; P T 1 w i n = 1 2 &#215; 1 2 + 1 2 &#215; 1 6 + 1 6 &#215; 1 2 = 5 12

Paragraph: Football teams $T_{1}$ and $T_{2}$ have to play two games against each other. It is assumed that…

Solution