Download App

Binomial Distribution — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsBinomial Distribution3 Marks
Question
In binomial distribution with five Bernoulli’s trials, the probability of one and two success are 0.4096 and 0.2048 respectively. Find the probability of success.
✓

Answer

Given: $X \sim B(n=5, p)$
The probability of $X$ success is
$
P(X=x)={ }^n \mathrm{C}_x p^x q^{n-x}, x=0,1,2, \ldots, n
$
i.e. $P(X=x)={ }^5 \mathrm{C}_x p^x q^{5-x}, x=0,1,2,3,4,5$
Probabilities of one and two successes are
$
P(X=1)={ }^5 C_1 p^1 q^{5-1}
$
and $P(X=2)={ }^5 \mathrm{C}_2 p^2 q^{5-2}$ respectively
Given: $P(X=1)=0.4096$ and $P(X=2)=0.2048$
$\therefore \frac{P(X=2)}{P(X=1)}=\frac{0.2048}{0.4096}$
i.e. $\frac{{ }^5 \mathrm{C}_2 p^2 q^{5-2}}{{ }^5 \mathrm{C}_1 p^2 q^{5-1}}=\frac{1}{2}$
i.e. $2 \times{ }^5 C_2 p^2 q^3=1 \times{ }^5 C_1 p q^4$
i.e. $2 \times \frac{5 \times 4}{1 \times 2} \times p^2 q^3=1 \times 5 \times p q^4$
i.e. $20 p^2 q^3=5 p q^4$
i.e. $4 p=q$
i.e. $4 p=1-p$
i.e. $5 p=1$
$
\therefore p=\frac{1}{5}
$
Hence, the probability of success is $\frac{1}{5}$.

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 "Solve the Following Question.(3 Marks)" from Binomial Distribution→Binomial Distribution — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

Find the general solutions of the following :

$4 \sin ^2 \theta=1$

→
A bag contains 4 red and 6 black balls. Three balls are drawn at random. Find the probability distribution of the number of red balls.
→
Passing through $(-1, 2)$ and perpendicular to the lines $x + 2y + 3 = 0$ and $3x – 4y – 5 = 0$.
→
Express $-\bar{i}-3 \bar{j}+4 \bar{k}$ as a linear combination of vectors $2 \bar{i}+\bar{j}-4 \bar{k}, 2 \bar{i}+3 \bar{k}$ and $3 \bar{i}+\bar{j}-2 \bar{k}$
→
Differentiate the following functions with respect to x:
$\tan^{-1}(\text{e}^{\text{x}})$
→
Find the approximate values of :

$\cot ^{-1}(0.999)$

→
For the following differntial equations verify that the accompanying function is a solution:
Differential equation Function
$\text{x}^3\frac{\text{d}{^2}\text{y}}{\text{dx}^2}=1$ $\text{y}=\text{ax}+\text{b}+\frac{1}{2\text{x}}$
→
Express $\overrightarrow{\text{AB}}$ in terms of unit vectors $\hat{\text{i}}\text{ and }\hat{\text{j}}$, when the point is:A(-6, 3), B(-2, -5)
Find $\Big|\overrightarrow{\text{AB}}\Big|$
→
Evalute the following integrals:
$\int\frac{\text{e}^{2\text{x}}}{\text{e}^{2\text{x}}-2}\text{dx}$
→
ABCD is a quadrilateral. Find the sum of the vectors $\overrightarrow{\text{BA}},\overrightarrow{\text{BC}},\overrightarrow{\text{CD}}\text{ and }\overrightarrow{\text{DA}}$.
→