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STD 12 - 13. probability — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 13. probability4 Marks
MCQ
Let a random variable $X$ have a binomial distribution with mean $8$ and variance $4$. If $P\left( {X \le 2} \right) = \frac{k}{{{2^{16}}}}$,  then $k$ is equal to
  • A
    $17$
  • ✓
    $137$
  • C
    $1$
  • D
    $121$
✓

Answer

Correct option: B.
$137$
b
$\mathrm{np}=8$

$\mathrm{npq}=4$

$\mathrm{q}=\frac{1}{2} \Rightarrow \mathrm{p}=\frac{1}{2}$

$n=16$

$p(x=r)=^{16} C_{r}\left(\frac{1}{2}\right)^{16}$

$p(x \leq 2)=\frac{^{16} C_{0}+^{16} C_{1}+^{16} C_{2}}{2^{16}}$

$=\frac{137}{2^{16}}$

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