Q62 / 200 · AP EAMCET 2001 · Mathematics

For a binominal variate $X$, if $n=4$ and $P(X=4)=6 P(X=2)$, then the value of $p$ is

  • A
    $\frac{3}{7}$
  • B
    $\frac{4}{7}$
  • Correct answer
    C
    $\frac{6}{7}$
  • D
    $\frac{5}{7}$

Solution

We have, $\begin{array}{rlrl} & P(X & =4)=6 P(X=2) \\ \Rightarrow & & { }^4 C_4 p^4 q^0 & =6 \cdot{ }^4 C_2 p^2 q^2 \\ \Rightarrow & & p^2 & =36 q^2 \\ \Rightarrow & & p & =6 q=6(1-p) \\ p & =\frac{6}{7}\end{array}$

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

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