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

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 13. probability4 Marks
MCQ
Let $X$ be a random variable having binomial distribution $B (7, p )$. If $P ( X =3)=5 P ( X =4)$, then the sum of the mean and the variance of $X$ is
  • A
    $\frac{105}{16}$
  • ✓
    $\frac{77}{36}$
  • C
    $\frac{7}{16}$
  • D
    $\frac{49}{16}$
✓

Answer

Correct option: B.
$\frac{77}{36}$
b
$B (7, p)$

$n =7 \quad p = p$

given

$P(x=3)=5 P(x=4)$

${ }^{7} C_{3} \times p^{3}(1-p)^{4}=5^{7} C_{4} p^{4}(1-p)^{3}$

$\frac{{ }^{7} C_{3}}{5 \times{ }^{7} C_{4}}=\frac{p}{1-p}$

$1- p =5 p$

$6 p =1$

$p=\frac{1}{6} \Rightarrow q=\frac{5}{6}$

$n =7$

Mean $= np =7 \times \frac{1}{6}=\frac{7}{6}$

Var $= npq =7 \times \frac{1}{6} \times \frac{5}{6}=\frac{35}{36}$

Sum

$=\frac{7}{6}+\frac{35}{36}$

$=\frac{42+35}{36}$

$=\frac{77}{36}$

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