Q81 / 160 · TS EAMCET 2009 · Mathematics

If $X$ is a binomial variate with the range $\{0,1,2,3,4,5,6\}$ and $P(X=2)=4 P(X=4)$, then the parameter $p$ of $X$ is

  • Correct answer
    A
    $\frac{1}{3}$
  • B
    $\frac{1}{2}$
  • C
    $\frac{2}{3}$
  • D
    $\frac{3}{4}$

Solution

Here, $n=6$ According to the question $\begin{array}{rlrl} { }^6 C_2 p^2 q^4=4 \cdot{ }^6 C_4 p^4 q^2 \\ \Rightarrow q^2 =4 p^2 \\ \Rightarrow (1-p)^2 & =4 p^2 \\ \Rightarrow 3 p^2+2 p-1 & =0 \\ \Rightarrow & (p+1)(3 p-1) & =0 \\ \Rightarrow & =\frac{1}{3} \\ & \because p \text { cannot be negative }) \end{array}$

Hence, the correct answer is option: 'A'.

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