MHT CET · Maths · Probability
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
- A \(\begin{array}{|c|c|c|c|}
\hline \mathrm{X}=x_{\mathrm{i}} & 0 & 1 & 2\mathrm{P}_{\mathrm{i}} & \frac{1}{36} & \frac{25}{36} & \frac{5}{18}\\ \hline\end{array}\) - B \(\begin{array}{|c|c|c|c|}
\hline \mathrm{X}=x_{\mathrm{i}} & 0 & 1 & 2\mathrm{P}_{\mathrm{i}} & \frac{25}{36} & \frac{1}{36} & \frac{5}{18} \\ \hline\end{array}\) - C \(\begin{array}{|c|c|c|c|}
\hline \mathrm{X}=x_{\mathrm{i}} & 0 & 1 & 2\mathrm{P}_{\mathrm{i}} & \frac{25}{36} & \frac{5}{18} & \frac{1}{36} \\ \hline \end{array}\) - D \(\begin{array}{|c|c|c|c|}
\hline \mathrm{X}=x_{\mathrm{i}} & 0 & 1 & 2\mathrm{P}_{\mathrm{i}} & \frac{5}{18} & \frac{1}{36} & \frac{25}{36} \\ \hline \end{array}\)
Answer & Solution
Correct Answer
(C) \(\begin{array}{|c|c|c|c|}
\hline \mathrm{X}=x_{\mathrm{i}} & 0 & 1 & 2\mathrm{P}_{\mathrm{i}} & \frac{25}{36} & \frac{5}{18} & \frac{1}{36} \\ \hline \end{array}\)
Step-by-step Solution
Detailed explanation
A fair die is tossed twice in succession.
\(\therefore \) 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.
\(\therefore \) Possible values of \(\mathrm{X}\) are: \(0,1,2\).
\(\therefore \) Probability distribution of \(\mathrm{X}\) is as follows:
\(\begin{array}{|c|c|c|c|} \hline \mathrm{X}=x_{\mathrm{i}} & 0 & 1 & 2 \\ \hline \mathrm{P}_{\mathrm{i}} & \frac{25}{36} & \frac{10}{36}=\frac{5}{18} & \frac{1}{36} \\ \hline \end{array}\)
\(\therefore \) 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.
\(\therefore \) Possible values of \(\mathrm{X}\) are: \(0,1,2\).
\(\therefore \) Probability distribution of \(\mathrm{X}\) is as follows:
\(\begin{array}{|c|c|c|c|} \hline \mathrm{X}=x_{\mathrm{i}} & 0 & 1 & 2 \\ \hline \mathrm{P}_{\mathrm{i}} & \frac{25}{36} & \frac{10}{36}=\frac{5}{18} & \frac{1}{36} \\ \hline \end{array}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- The equation of the line passing through the point \((-1,3,-2)\) and perpendicular to each of the lines \(\frac{x}{1}=\frac{y}{2}=\frac{z}{3}\) and \(\frac{x+2}{-3}=\frac{y-1}{2}=\frac{z+1}{5}\) isMHT CET 2023 Easy
- If the L. M. V. T. holds for the function \(f(x)=x+\frac{1}{x}, x \in[1,3]\), then c=MHT CET 2020 Easy
- \(\int \frac{(5 \sin \theta-2) \cos \theta}{\left(5-\cos ^2 \theta-4 \sin \theta\right)} d \theta=\)MHT CET 2025 Medium
- If the Cartesian equation of a line is \(6 x-2=3 y+1=2 z-2\), then the vector equation of the line isMHT CET 2023 Easy
- The area of the region bounded by the curves \(y=\mathrm{e}^x, y=\log x\) and lines \(x=1, x=2\) isMHT CET 2023 Hard
- Negation of inverse of the following statement pattern \((p \wedge q) \rightarrow(p \vee \sim q)\) isMHT CET 2023 Easy
More PYQs from MHT CET
- Identify the chiral molecule from following.MHT CET 2023 Easy
- The direction cosines of a normal to the plane passing throgh \((4,2,3)\), \((-1,4,2)\) and \((3,2,1)\) are .....MHT CET 2025 Medium
- If \(\frac{x^2}{\mathrm{a}}+\frac{2 x y}{\mathrm{~h}}+\frac{y^2}{\mathrm{~b}}=0\) represents a pair of straight lines and slope of one of the lines is twice that of the other, then \(a b: h^2\) is
[Note: The question has been modified to get the correct answer.]MHT CET 2024 Medium - Which one of the following is NOT the main postulate of Darwinism?MHT CET 2023 Medium
- In a Young's double slit experiment wavelength of light used is \(6000 Å\). The first order maxima and tenth order maxima fall at 14.50 mm and 16.75 mm from the particular reference point in the interference pattern respectively. If the wavelength is changed to \(5500 Å\) then the position of zero order and tenth order maxima are respectively [The other arrangements remaining same]MHT CET 2025 Medium
- If two planets have their radii in the ratio \(x: y\) and densities in the ratio \(m: n\), then the acceleration due to gravity on them are in the ratioMHT CET 2023 Medium