(B) The probability of a bad reaction is $p = 0.01$ and the number of people is $n = 300$. Since $n$ is large and $p$ is small,we use the Poisson dist

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(B) The probability of a bad reaction is $p = 0.01$ and the number of people is $n = 300$. Since $n$ is large and $p$ is small,we use the Poisson distribution as an approximation to the binomial distribution. The mean $\mu$ is given by $\mu = n \times p = 300 \times 0.01 = 3$. The Poisson probability formula is $P(X = x) = \frac{e^{-\mu} \cdot \mu^x}{x!}$. For $x = 2$,we have $P(X = 2) = \frac{e^{-3} \cdot 3^2}{2!} = \frac{9}{2 e^3}$.

Class 12 Mathematics Probability Probability distribution

Easy

If the probability of a bad reaction from a vaccination is $0.01$,then the probability that exactly two out of $300$ people will get a bad reaction is

TS EAMCET 2018 All TS EAMCET

A
$\frac{7}{2 e^3}$
B
$\frac{9}{2 e^3}$
C
$\frac{7}{e^3}$
D
$\frac{9}{e^3}$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Probability

Subtopic

Probability distribution

Previous Year

TS EAMCET 2018 Paper All TS EAMCET years →

Let the mean and standard deviation of the probability distribution given by the table below be $\mu$ and $\sigma$ respectively. If $\sigma - \mu = 2$,then find the value of $\sigma$.
$X=x$ $-3$ $0$ $1$ $\alpha$
$P(X=x)$ $\frac{1}{4}$ $K$ $\frac{1}{4}$ $\frac{1}{3}$

MediumMHT CET 2025

View Solution

The cumulative distribution function (c.d.f.) $F(x)$ of a discrete random variable $X$ is given by the following table:
$X$ $-3$ $-1$ $0$ $1$ $3$ $5$ $7$ $9$
$F(X)$ $0.1$ $0.3$ $0.5$ $0.65$ $0.75$ $0.85$ $0.90$ $1$

Then,find $P[X=3]$.

$X$	$-3$	$-1$	$0$	$1$	$3$	$5$	$7$	$9$
$F(X)$	$0.1$	$0.3$	$0.5$	$0.65$	$0.75$	$0.85$	$0.90$	$1$

EasyMHT CET 2020

View Solution

On an average,if one out of $100$ electric bulbs produced by a company is found to be defective,then the probability that there are at least two defective bulbs in a consignment of $600$ bulbs is:

MediumAP EAMCET 2017

View Solution

For the probability distribution of a discrete random variable $X$ as given below,the mean of $X$ is:
$X = x$ $-2$ $-1$ $0$ $1$ $2$ $3$
$P(X = x)$ $\frac{1}{10}$ $K + \frac{2}{10}$ $K + \frac{3}{10}$ $K + \frac{3}{10}$ $K + \frac{4}{10}$ $K + \frac{2}{10}$

$X = x$	$-2$	$-1$	$0$	$1$	$2$	$3$
$P(X = x)$	$\frac{1}{10}$	$K + \frac{2}{10}$	$K + \frac{3}{10}$	$K + \frac{3}{10}$	$K + \frac{4}{10}$	$K + \frac{2}{10}$

MediumAP EAMCET 2024

View Solution

$A$ fair die with numbers $1$ to $6$ on its faces is thrown. Let $X$ denote the number of factors of the number on the uppermost face. Then the probability distribution of $X$ is

EasyMHT CET 2023

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$X=x$	$-3$	$0$	$1$	$\alpha$
$P(X=x)$	$\frac{1}{4}$	$K$	$\frac{1}{4}$	$\frac{1}{3}$

If the probability of a bad reaction from a vaccination is $0.01$,then the probability that exactly two out of $300$ people will get a bad reaction is

Similar Questions

Let the mean and standard deviation of the probability distribution given by the table below be $\mu$ and $\sigma$ respectively. If $\sigma - \mu = 2$,then find the value of $\sigma$.$X=x$$-3$$0$$1$$\alpha$$P(X=x)$$\frac{1}{4}$$K$$\frac{1}{4}$$\frac{1}{3}$

The cumulative distribution function (c.d.f.) $F(x)$ of a discrete random variable $X$ is given by the following table:$X$$-3$$-1$$0$$1$$3$$5$$7$$9$$F(X)$$0.1$$0.3$$0.5$$0.65$$0.75$$0.85$$0.90$$1$Then,find $P[X=3]$.

On an average,if one out of $100$ electric bulbs produced by a company is found to be defective,then the probability that there are at least two defective bulbs in a consignment of $600$ bulbs is:

For the probability distribution of a discrete random variable $X$ as given below,the mean of $X$ is:$X = x$$-2$$-1$$0$$1$$2$$3$$P(X = x)$$\frac{1}{10}$$K + \frac{2}{10}$$K + \frac{3}{10}$$K + \frac{3}{10}$$K + \frac{4}{10}$$K + \frac{2}{10}$

$A$ fair die with numbers $1$ to $6$ on its faces is thrown. Let $X$ denote the number of factors of the number on the uppermost face. Then the probability distribution of $X$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module

Let the mean and standard deviation of the probability distribution given by the table below be $\mu$ and $\sigma$ respectively. If $\sigma - \mu = 2$,then find the value of $\sigma$.
$X=x$ $-3$ $0$ $1$ $\alpha$
$P(X=x)$ $\frac{1}{4}$ $K$ $\frac{1}{4}$ $\frac{1}{3}$

The cumulative distribution function (c.d.f.) $F(x)$ of a discrete random variable $X$ is given by the following table:
$X$ $-3$ $-1$ $0$ $1$ $3$ $5$ $7$ $9$
$F(X)$ $0.1$ $0.3$ $0.5$ $0.65$ $0.75$ $0.85$ $0.90$ $1$

Then,find $P[X=3]$.

For the probability distribution of a discrete random variable $X$ as given below,the mean of $X$ is:
$X = x$ $-2$ $-1$ $0$ $1$ $2$ $3$
$P(X = x)$ $\frac{1}{10}$ $K + \frac{2}{10}$ $K + \frac{3}{10}$ $K + \frac{3}{10}$ $K + \frac{4}{10}$ $K + \frac{2}{10}$