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

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

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

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

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

$=1320$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Similar questions

If $a, b, c$  are all different and $\left| {\,\begin{array}{*{20}{c}}a&{{a^3}}&{{a^4} - 1}\\b&{{b^3}}&{{b^4} - 1}\\c&{{c^3}}&{{c^4} - 1}\end{array}\,} \right|$ = $0$ , then the value of $abc(ab + bc + ca)$ is
The derivative of $\cos ^{-1}\left(2 x^2-1\right)$ w.r.t. $\cos ^{-1} x$ is
Four numbers are chosen at random ( without replacement ) from the set $\{1,2,3,..,20\}$

Statement $-1 :$ The probability that the chosen numbers when arranged in some order will form an $A.P.$ is $\frac{1}{{85}}$ . 

Statement $-2 :$ If the four chosen numbers form an $A.P.$, then the set of all possible values of common difference is $\left( { \pm 1, \pm 2, \pm 3, \pm 4, \pm 5} \right)$ છે.

If $f(x) = {x^2} + 1$, then $fof(x)$ is equal to
If the matrix $\left[ {\begin{array}{*{20}{c}}0&1&{ - 2}\\{ - 1}&0&3\\\lambda &{ - 3}&0\end{array}} \right]$ is singular, then $\lambda $=
The differential equation $2xy\,\, dy = (x^2 + y^2 + 1) dx$ determines
The solution of the differential equation $\frac{\text{dy}}{\text{dx}}-\text{Ky}=0, \text{y}(0)=1$ approaches to zero when $\text{x}\rightarrow\propto$ if,
  1. K = 0
  2. K > 0
  3. K < 0
  4. None of these.
If system of equations $kx + 2y - z = 2,$$\left( {k - 1} \right)x + ky + z = 1,x + \left( {k - 1} \right)y + kz = 3$ has only one solution, then number of possible real value$(s)$ of $k$ is -
 
The number of arbitrary constants in the particular solution of a differential equation of third order are _________.
The magnitude of the vector 6i + 2j + 3k is equal to:
  1. 5
  2. 1
  3. 7
  4. 12