If a random variable X follows the Binomial distribution B (33, p… - Vidyadip

MCQ

If a random variable $X$ follows the Binomial distribution $B (33, p )$ such that $3 P ( X =0)= P ( X =1)$, then the value of $\frac{ P ( X =15)}{ P ( X =18)}-\frac{ P ( X =16)}{ P ( X =17)}$ is equal to

✓
$1320$
B
$1088$
C
$\frac{120}{1331}$
D
$\frac{1088}{1089}$

✓

Answer

Correct option: A.

$1320$

a
$n =33$, let probability of success is $p$ and $q =1- p$

$3 p ( x =0)= p ( x =1)$

3. ${ }^{33} C _{0}( q )^{33}={ }^{33} C _{1} pq ^{32}$

$p =\frac{1}{12}, q =\frac{11}{12}, \frac{ q }{ p }=11$

$\frac{ p ( x =15)}{ p ( x =18)}-\frac{ p ( x =16)}{ p ( x =17)}$

$\frac{{ }^{33} C_{15} p^{15} q^{18}}{{ }^{33} C_{18} p^{18} q^{15}}-\frac{{ }^{33} C_{16} p^{16} q^{17}}{{ }_{17} P ^{17} q^{16}}=\left(\frac{q}{p}\right)^{3}-\left(\frac{q}{p}\right)$

$=(11)^{3}-11$

$=1320$

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