AP EAMCET · Maths · Probability
If \(\mathrm{X}\) is random variable with probability distribution \(P(X=k)=\frac{(k+1) c}{2^k}, k=0,1,2, \ldots\), then \(P(X \geq 3)=\)
- A \(\frac{1}{4}\)
- B \(\frac{5}{16}\)
- C \(\frac{5}{11}\)
- D \(\frac{3}{16}\)
Answer & Solution
Correct Answer
(B) \(\frac{5}{16}\)
Step-by-step Solution
Detailed explanation
\text { } \begin{gathered} \because P(X=k)=\frac{(k+1) C}{2^k}, k=0,1,2, \ldots . \\ \sum P(X=\mathrm{k})=\mathrm{C}\left(1+\frac{2}{2}+\frac{3}{2^2}+\frac{4}{2^3}+\ldots\right) \\ \Rightarrow 1=C\left(1+\frac{2}{2}+\frac{3}{2^2}+\frac{4}{2^3}+\ldots\right) \\ \Rightarrow…
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
- One card is selected at random from cards numbered form to . What is the probability that the number on the card is even or divisible by .AP EAMCET 2021 Easy
- If the equation of the circle lying in the first quadrant, touching both the coordinate axes and the line \(\frac{x}{3}+\frac{y}{4}=1\) is \((x-c)^2+(y-c)^2=c^2\), then \(c=\)AP EAMCET 2025 Medium
- If \(y^2+z^2=a y z, z^2+x^2=b x z, x^2+y^2=c x y\), then the value of \(\frac{x z}{y^2}+\frac{y^2}{z x}\) isAP EAMCET 2022 Medium
- If \(a, b\) and \(c\) are the sides of \(\triangle A B C\) for which \(r_1=8, r_2=12\) and \(r_3=24\), then the ordered triad \((a, b, c)=\)AP EAMCET 2019 Medium
- The diagonals \(\mathrm{AC}\) and \(\mathrm{BD}\) of a rhombus \(\mathrm{ABCD}\) intersect at the point \((3,4)\). If \(\mathrm{BD}=2 \sqrt{2}, \mathrm{~A}=(1,2), \mathrm{B}=(\alpha, \beta)\),\(D=(\gamma, \delta)\) and \(\alpha < \delta < \gamma < \beta\), then \(\beta+\gamma-\delta=\)AP EAMCET 2023 Medium
- The probability that a person chosen at random is left handed (in hand writing) is 0.1 . Then the probability that in a group of 10 people there is a left handed person isAP EAMCET 2023 Easy
More PYQs from AP EAMCET
- Which of the following behaves as a Lewis acid?AP EAMCET 2022 Easy
- If \(P=(0,1,0), Q=(0,0,1)\), then the projection of \(P Q\) on the plane \(x+y+z=3\) isAP EAMCET 2002 Medium
- \(\int \frac{\cos ^3 x+\cos ^5 x}{\sin ^2 x+\sin ^4 x} d x=\)AP EAMCET 2018 Medium
- If \(\mathrm{f}(\mathrm{x})\) is a function such that \(\mathrm{f}^{\prime}(\mathrm{x})=\sqrt{\mathrm{f}^2(\mathrm{x})-1}\) and \(f(0)=1\), then \(f(1)=\)AP EAMCET 2023 Medium
- The material used in nuclear industry as protective shields and control rods isAP EAMCET 2017 Medium
- A planet is revolving around the Sun as shown in the figure. The radius vectors joining the Sun and the planet at points \(A\) and \(B\) are \(90 \times 10^6 \mathrm{~km}\) and \(60 \times 10^6 \mathrm{~km}\), respectively. The ratio of velocities of the planet at the points \(A\) and \(B\) when its velocities make angle \(30^{\circ}\) and \(60^{\circ}\) with major-axis of the orbit is
AP EAMCET 2019 Medium