GO Classes Test Series 2024 | Mock GATE | Test 13 | Question: 44

Answer 1

There are $9$ possible outcomes. Write down all $9$ possible outcomes for $\text{T}_1$ and corresponding $X$ and $Y$.
$$
\begin{array}{c|c|c|c}
\hline \textbf{1st Match} & \textbf{2nd Match} & \textbf{X} & \textbf{Y} \\
\hline \mathrm{w} & \mathrm{w} & 6 & 0 \\
\mathrm{w} & \mathrm{d} & 4 & 1 \\
\mathrm{w} & \mathrm{l} & 3 & 3 \\
\mathrm{~d} & \mathrm{w} & 4 & 1 \\
\mathrm{~d} & \mathrm{~d} & 2 & 2 \\
\mathrm{~d} & \mathrm{l} & 1 & 4 \\
\mathrm{l} & \mathrm{w} & 3 & 3 \\
\mathrm{l} & \mathrm{d} & 1 & 4 \\
\mathrm{l} & \mathrm{l} & 0 & 6 \\
\hline
\end{array}
$$
From the above table, we have

$P(X=Y)=P(w l)+P(d d)+p(l w)= P(w) P(l)+P(d) P(d)+P(l) P(w)$

$ = 1 / 2 * 1 / 3+1 / 6 * 1 / 6+1 / 3 * 1 / 2=13 / 36$