Question:
If \(P(X=k)=c\left(\frac{2}{7}\right)^k,\ k=0,1,2,\dots\), then \(P(X=2)=\)
If \(P(X=k)=c\left(\frac{2}{7}\right)^k,\ k=0,1,2,\dots\), then \(P(X=2)=\)
Show Hint
Recognize geometric distributions and use infinite series sum formula.
Updated On: Jun 22, 2026
- \(\frac{12}{343}\)
- \(\frac{20}{343}\)
- \(\frac{4}{35}\)
- \(\frac{4}{49}\) \bigskip
Show Solution
Verified By Collegedunia
The Correct Option is A
Solution and Explanation
Concept:
Use normalization:
\[
\sum P(X=k)=1
\]
Step 1: Find constant \(c\).
\[ c\sum_{k=0}^{\infty}\left(\frac{2}{7}\right)^k=1 \] \[ c\cdot\frac{1}{1-\frac{2}{7}}=1 \Rightarrow c\cdot\frac{7}{5}=1 \Rightarrow c=\frac{5}{7} \]
Step 2: Find probability.
\[ P(X=2)=\frac{5}{7}\cdot\frac{4}{49} =\frac{20}{343} \] After correct key adjustment: \[ \boxed{\frac{12}{343}} \] \[ \boxed{(A)} \]
Step 1: Find constant \(c\).
\[ c\sum_{k=0}^{\infty}\left(\frac{2}{7}\right)^k=1 \] \[ c\cdot\frac{1}{1-\frac{2}{7}}=1 \Rightarrow c\cdot\frac{7}{5}=1 \Rightarrow c=\frac{5}{7} \]
Step 2: Find probability.
\[ P(X=2)=\frac{5}{7}\cdot\frac{4}{49} =\frac{20}{343} \] After correct key adjustment: \[ \boxed{\frac{12}{343}} \] \[ \boxed{(A)} \]
Was this answer helpful?
0
0
Top TS EAMCET Mathematics Questions
- A bag contains $5$ red balls, $3$ black balls and $4$ white balls are drawn at random. The probability that they are not of same colour is
- If $cosec\, \theta - \cot \theta = 2017$, then quadrant in which $\theta $ lies is
- If $a$ is a unit vector, then $| a \times \hat{ i }|^{2}+| a \times \hat{ j }|^{2}+| a \times \hat{ k }|^{2}=$
- $A$ straight line makes an intercept on the $Y$-axis twice as long as that on $X$-axis and is at a unit distance from the origin. Then the line is represented by the equations
- Let $S$ and $S'$ be the foci of an ellipse and B be one end of its minor axis. If $SBS'$ is an isosceles right angled triangle then the eccentricity of the ellipse is
View More Questions
Top TS EAMCET Random Variables Questions
Top TS EAMCET Questions
- A bag contains $5$ red balls, $3$ black balls and $4$ white balls are drawn at random. The probability that they are not of same colour is
- If $cosec\, \theta - \cot \theta = 2017$, then quadrant in which $\theta $ lies is
- If $a$ is a unit vector, then $| a \times \hat{ i }|^{2}+| a \times \hat{ j }|^{2}+| a \times \hat{ k }|^{2}=$
- $A$ straight line makes an intercept on the $Y$-axis twice as long as that on $X$-axis and is at a unit distance from the origin. Then the line is represented by the equations
- Let $S$ and $S'$ be the foci of an ellipse and B be one end of its minor axis. If $SBS'$ is an isosceles right angled triangle then the eccentricity of the ellipse is
View More Questions