If in a binomial distribution n=4,P(X=0)=16 81 , then P(X=4) equa… - Vidyadip

MCQ

If in a binomial distribution $\text{n}=4,\text{P(X}=0)=\frac{16}{81},$ then $\text{P(X}=4)$ equals:

A
$\frac{1}{16}$
B
$\frac{1}{81}$
C
$\frac{1}{27}$
D
$\frac{1}{8}$

✓

Answer

$\frac{1}{81}$

Solution:

Given $\text{n}=4,\text{P(X}=0)=\frac{16}{81}$

$\text{P(X}=0)=\frac{16}{81}$

$\text{ }^5\text{C}_0\text{p}^0\text{q}^4=\frac{16}{81}$

$\text{q}^4=\frac{16}{81}$

$\text{q}=\frac{2}{3}\Rightarrow\text{p}=\frac{1}{3}$

$\Rightarrow\text{P(X}=4)=\text{ }^5\text{C}_4\big(\frac{1}{4}\big)^4=\frac{1}{81}$

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

Explore more

More "M.C.Q (1 Marks)" from Probability→Probability — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\int {\sqrt 2 \sqrt {1 + \sin x} } \,\,dx = - \,4\cos (ax + b) + c$ then the value of $(a, b) $ is

If $f(x)=\left\{\begin{array}{l}x, \text { if } x \leq 1 \\ 7, \text { if } x>1\end{array}\right.$, then

If $\text{f(x)}=\begin{cases}\frac{\log(1+\text{ax})-\log(1-\text{bx})}{\text{x}},&\text{x}\neq0\\\text{k},&\text{x}=0\end{cases}$ and f(x) is continous at x = 0, then the value of k is:

a - b
a + b
$\log\text{a}+\log\text{b}$
none of these

If $f(a+b+1-x)=f(x),$ for all $x,$ where $a$ and $b$ are fixed positive real numbers, then $\frac{1}{a+b} \int\limits_{a}^{b} x(f(x)+f(x+1)) d x$ is equal to

The area bounded by the curve y = f(x), x-axis, and the ordinates x = 1 and $(\text{b}-1)\sin(3\text{b}+4)$ Then, f(x) is:

$(\text{x}-1)\cos(3\text{x}+4)$
$\sin(3\text{x}+4)$
$\sin(3\text{x}+4)+3(\text{x}-1)\cos(3\text{x}+4)$
none of these

For linear programming problem, the objective function is $Z=3 x+2 y$. If the comer points of the bounded feasible region are $(12,0),(4,2)$. $(1,5)$ and $(1,10)$, then the maximum value of $Z$ is ____________ .

If $A$ and $B$ are two independent events, then the probability of occurrence of atleast one of $A$ and $B$ is given by

A relation R is defined from {2, 3, 4, 5} to {3, 6, 7, 10} by : xRy ⇔ x is relatively prime to y. Then, domain of R is:

{2, 3, 5}
{3, 5}
{2, 3, 4}
{2, 3, 4, 5}

The equation of the plane parallel to the lines x - 1 = 2y - 5 = 2z and 3x = 4y - 11 = 3z -4 and passing through the point (2, 3, 3) is:

If $f(x) = \sin \log x$, then the value of $f(xy) + f\left( {\frac{x}{y}} \right) - 2f(x).\cos \log y$ is equal to