Q69 / 150 · MHT CET 2011 · Mathematics

If $x$ follows the Binomial distribution with parameters $n=6$ and $p$ and $9 P(X=4)$ $=P(X=2)$, then $p$ is

  • Correct answer
    A
    $1 / 4$
  • B
    $1 / 3$
  • C
    $1 / 2$
  • D
    $2 / 3$

Solution

Given, $9 P(X=4)=P(X=2)$ $\therefore \quad 9 \cdot{ }^{6} C_{4} p^{4}(1-p)^{2}={ }^{6} C_{2} p^{2}(1-p)^{4}$ $\Rightarrow \quad \frac{(1-p)^{2}}{p^{2}}=9$ $\Rightarrow \quad \frac{1-p}{p}=3$ $\Rightarrow \quad p=1 / 4$

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

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