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Question: Answered & Verified by Expert
A fair die is tossed twice in succession. If $\mathrm{X}$ denotes the number of fours in two tosses, then the probability distribution of $\mathrm{X}$ is given by
MathematicsProbabilityMHT CETMHT CET 2023 (11 May Shift 2)
Options:
  • A \begin{array}{|c|c|c|c|}
    \hline \mathrm{X}=x_{\mathrm{i}} & 0 & 1 & 2 \\
    \hline \mathrm{P}_{\mathrm{i}} & \frac{1}{36} & \frac{25}{36} & \frac{5}{18} \\
    \hline
    \end{array}
  • B \begin{array}{|c|c|c|c|}
    \hline \mathrm{X}=x_{\mathrm{i}} & 0 & 1 & 2 \\
    \hline \mathrm{P}_{\mathrm{i}} & \frac{25}{36} & \frac{1}{36} & \frac{5}{18} \\
    \hline
    \end{array}
  • C \begin{array}{|c|c|c|c|}
    \hline \mathrm{X}=x_{\mathrm{i}} & 0 & 1 & 2 \\
    \hline \mathrm{P}_{\mathrm{i}} & \frac{25}{36} & \frac{5}{18} & \frac{1}{36} \\
    \hline
    \end{array}
  • D \begin{array}{|c|c|c|c|}
    \hline \mathrm{X}=x_{\mathrm{i}} & 0 & 1 & 2 \\
    \hline \mathrm{P}_{\mathrm{i}} & \frac{5}{18} & \frac{1}{36} & \frac{25}{36} \\
    \hline
    \end{array}
Solution:
1493 Upvotes Verified Answer
The correct answer is: \begin{array}{|c|c|c|c|}
\hline \mathrm{X}=x_{\mathrm{i}} & 0 & 1 & 2 \\
\hline \mathrm{P}_{\mathrm{i}} & \frac{25}{36} & \frac{5}{18} & \frac{1}{36} \\
\hline
\end{array}
A fair die is tossed twice in succession.
$\therefore \quad$ Sample space (S)
$\begin{aligned}
= & (1,1),(1,2),(1,3),(1,4),(1,5),(1,6), \\
& (2,1),(2,2),(2,3),(2,4),(2,5),(2,6), \\
& (3,1),(3,2),(3,3),(3,4),(3,5),(3,6), \\
& (4,1),(4,2),(4,3),(4,4),(4,5),(4,6), \\
& (5,1),(5,2),(5,3),(5,4),(5,5),(5,6), \\
& (6,1),(6,2),(6,3),(6,4),(6,5),(6,6)\}
\end{aligned}$
$X:$ Number of fours in two tosses.
$\therefore \quad$ Possible values of $\mathrm{X}$ are: $0,1,2$.
$\therefore \quad$ Probability distribution of $\mathrm{X}$ is as follows:
\begin{array}{|c|c|c|c|}
\hline \mathrm{X}=x_{\mathrm{i}} & 0 & 1 & 2 \\
\hline \mathrm{P}_{\mathrm{i}} & \frac{25}{36} & \frac{10}{36}=\frac{5}{18} & \frac{1}{36} \\
\hline
\end{array}

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