JEE Mains · Maths · STD 12 - 13. probability
If the probability that the random variable X takes the value \(x\) is given by \(P(X=x)=k(x+1) 3^{-x}\), \(\mathrm{x}=0,1,2,3 \ldots \ldots\), where k is a constant, then \(\mathrm{P}(\mathrm{X} \geq 3)\) is equal to
- A \(\frac{7}{27}\)
- B \(\frac{4}{9}\)
- C \(\frac{8}{27}\)
- D \(\frac{1}{9}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{9}\)
Step-by-step Solution
Detailed explanation
\(\sum_{x=0}^{\infty} k(x+1) 3^{-x}=1\) \(\Rightarrow \frac{1}{\mathrm{k}}=1+\frac{2}{3}+\frac{3}{3^2}+\frac{4}{3^3}+\) ...(i) \(\frac{1}{3 \mathrm{k}}=\frac{1}{3}+\frac{2}{3^2}+\frac{3}{3^3}+\ldots\) ...(ii) (i)- (ii)…
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
- Let \(A=\{-3,-2,-1,0,1,2,3\),\(\} . Let R\) be a relation on A defined by \(x R y\) if and only if \(0 \leq x^2+2 y \leq 4\).
Let \(l\) be the number of elements in R and \(m\) be the minimum number of elements required to be added in R to make it a reflexive relation. then \(l+m\) is equal toJEE Mains 2025 Medium - Let \(P_{1}, P_{2}, \ldots \ldots, P_{15}\) be \(15\) points on a circle. The number of distinct triangles formed by points \(P_{i}, P_{j}, P_{k}\) such that \(i+j+k \neq 15\), is :JEE Mains 2021 Hard
- The volume of the largest possible right circular cylinder that can be inscribed in a sphere of radius \( = \sqrt 3 \) isJEE Mains 2014 Hard
- The distance of the point \((1, 0, 2)\) from the point of intersection of the line \(\frac{{x - 2}}{3} = \frac{{y + 1}}{4} = \frac{{z - 2}}{{12}}\) and the plane \(x - y + z = 16\) isJEE Mains 2015 Medium
- Let \(f:[-1,1] \rightarrow R\) be defined as \(f(x)=a x^{2}+b x+c\) for all \(x \in[-1,1],\) where \(a , b , c \in R\) such that \(f (-1)=2, f ^{\prime}(-1)=1\) and for \(x \in(-1,1)\) the maximum value of \(f ^{\prime \prime}( x )\) is \(\frac{1}{2} .\) If \(f ( x ) \leq \alpha\) , \(x \in[-1,1],\) then the least value of \(\alpha\) is equal to ...... .JEE Mains 2021 Hard
- If the length of the latus rectum of an ellipse is \(4\,units\) and the distance between a focus and its nearest vertex on the major axis is \(\frac {3}{2}\,units\) , then its eccentricity is?JEE Mains 2018 Hard
More PYQs from JEE Mains
- The number of non-empty equivalence relations on the set \(\{1,2,3\}\) is :JEE Mains 2025 Easy
- The number of distinct real roots of the equation \(|\mathrm{x}+1||\mathrm{x}+3|-4|\mathrm{x}+2|+5=0\), is ...........JEE Mains 2024 Hard
- Let the position vectors of three vertices of a triangle be \(4 \vec{p}+\vec{q}-3 \vec{r},-5 \vec{p}+\vec{q}+2 \vec{r}\) and \(2 \overrightarrow{\mathrm{p}}-\overrightarrow{\mathrm{q}}+2 \overrightarrow{\mathrm{r}}\). If the position vectors of the orthocenter and the circumcenter of the triangle are \(\frac{\vec{p}+\vec{q}+\vec{r}}{4}\) and \(\alpha \vec{p}+\beta \vec{q}+\gamma \vec{r}\) respectively, then \(\alpha+2 \beta+5 \gamma\) is equal to :JEE Mains 2025 Hard
- A box contains 10 pens of which 3 are defective. A sample of 2 pens is drawn at random and let \(X\) denote the number of defective pens. Then the variance of X isJEE Mains 2025 Easy
- The number of real roots of the equation \(\mathrm{x}|\mathrm{x}-2|+3|\mathrm{x}-3|+1=0\) is :JEE Mains 2025 Medium
- If the minimum value of \(f(x)=\frac{5 x^{2}}{2}+\frac{\alpha}{x^{5}}, x>0\), is 14 , then the value of \(\alpha\) is equal to.JEE Mains 2022 Hard