Question
Let $X \sim B(10,0.2)$. Find
(a) $\quad P(X=1)$
(b) $\quad P(X \geq 1)$
(a) $\quad P(X=1)$
(b) $\quad P(X \geq 1)$
✓
Answer
$X \sim B(10,0.2)$
$\therefore\quad n=10, \quad p=0.2$
$\therefore\quad q=1-p=1-0.2=0.8$
$\therefore \quad P(X=x)={ }^{10} C_x(0.2)^x \times(0.8)^{10-x} \quad P(X=x)={ }^n C_x \cdot p^x \times q^{n-x}$
$\therefore \quad P(X=1)={ }^{10} C_1(0.2)^1 \times(0.8)^{10-1}$
$\therefore\quad=10 \times 0.2 \times(0.8)^9$
$\therefore\quad P(X=1)=2 \times(0.8)^9$
$\therefore\quad P(X \geq 1)=1-P(X=0)$
$\therefore\quad=1-{ }^{10} C_0(0.2)^0 \times(0.8)^{10-0}$
$\therefore\quad=1-1 \times 1 \times(0.8)^{10}$
$\therefore\quad P(X \geq 1)=1-(0.8)^{10}$
$\therefore\quad n=10, \quad p=0.2$
$\therefore\quad q=1-p=1-0.2=0.8$
$\therefore \quad P(X=x)={ }^{10} C_x(0.2)^x \times(0.8)^{10-x} \quad P(X=x)={ }^n C_x \cdot p^x \times q^{n-x}$
$\therefore \quad P(X=1)={ }^{10} C_1(0.2)^1 \times(0.8)^{10-1}$
$\therefore\quad=10 \times 0.2 \times(0.8)^9$
$\therefore\quad P(X=1)=2 \times(0.8)^9$
$\therefore\quad P(X \geq 1)=1-P(X=0)$
$\therefore\quad=1-{ }^{10} C_0(0.2)^0 \times(0.8)^{10-0}$
$\therefore\quad=1-1 \times 1 \times(0.8)^{10}$
$\therefore\quad P(X \geq 1)=1-(0.8)^{10}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
If $|\vec{\text{a}}|=\text{a}$ and $\big|\vec{\text{b}}\big|=\text{b},$ prove that $\Big(\frac{\vec{\text{a}}}{\text{a}^2}-\frac{\vec{\text{b}}}{\text{b}^2}\Big)^2=\Big(\frac{\vec{\text{a}}-\vec{\text{b}}}{\text{ab}}\Big)^2.$
→For each of the following differential equations, find the particular solution satisfying the given condition:
→$y (1+\log x ) \frac{d x}{d y}- x \log x =0, y = e ^2$, when $x = e$
If $\text{A}=\begin{bmatrix}3&1\\-1&2\end{bmatrix}$ and $\text{I}=\begin{bmatrix}1&0\\0&1\end{bmatrix},$ then find $\lambda$ so that $\text{A}^2 = 5\text{A} + \lambda\text{I}.$
→Solve the following differential equations:$2\text{x}\frac{\text{dy}}{\text{dx}}=5\text{y},\text{y}(1)=1$
→If a matrix has 8 elements, what are the possible orders it can have? What if it has 5 elements?
Evaluate: $\int_0^{\frac{\pi}{2}} \frac{\cos x}{(1+\sin x)(2+\sin x)} d x$
→Find a vector of magnitude of 5 units parallel to the resultant of the vectors $\vec{\text{a}}=2\hat{\text{i}}+3\hat{\text{j}}-\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-2\hat{\text{j}}+\hat{\text{k}}$.
→Find the expected value, variance, and standard deviation of the random variable whose p.m.f’s are given below:
Write a value of $\int\text{x}^2\sin\text{x}^3\text{ dx}$
→Evalute the following integrals:
$\int\frac{10\text{x}^9+10^\text{x}\log_\text{e}10}{10^\text{x}+\text{x}^{10}}\text{dx}$
→$\int\frac{10\text{x}^9+10^\text{x}\log_\text{e}10}{10^\text{x}+\text{x}^{10}}\text{dx}$