(A) The given probability mass function is $P(X = x) = \frac{^5C_x}{2^5}$.This is a binomial distribution $B(n, p)$ with $n = 5$ and $p = 0.5$.Calcula

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

(A) The given probability mass function is $P(X = x) = \frac{^5C_x}{2^5}$.This is a binomial distribution $B(n, p)$ with $n = 5$ and $p = 0.5$.Calculate $P(X \leq 2) = P(X=0) + P(X=1) + P(X=2) = \frac{^5C_0 + ^5C_1 + ^5C_2}{2^5} = \frac{1 + 5 + 10}{32} = \frac{16}{32} = 0.5$.Calculate $P(X \geq 3) = P(X=3) + P(X=4) + P(X=5) = \frac{^5C_3 + ^5C_4 + ^5C_5}{2^5} = \frac{10 + 5 + 1}{32} = \frac{16}{32} = 0.5$.Since $P(X \leq 2) = 0.5$ and $P(X \geq 3) = 0.5$, we have $P(X \leq 2) = P(X \geq 3)$.

Class 12 Mathematics Probability Binomial distribution

Difficult

The probability mass function of a random variable $X$ is given by $P(X = x) = \frac{^5C_x}{2^5}$, for $x = 0, 1, 2, 3, 4, 5$ and $0$ otherwise. Which of the following is correct?

MHT CET 2026 All MHT CET

A
$P(X \leq 2) = P(X \geq 3)$
B
$P(X \leq 2) > P(X \geq 3)$
C
$P(X \leq 2) < P(X \geq 3)$
D
$P(X \leq 2) = 2P(X \geq 3)$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Probability

Subtopic

Binomial distribution

Previous Year

MHT CET 2026 Paper All MHT CET years →

The probability that a student is not a swimmer is $\frac{1}{5}$. Then the probability that out of five students,four are swimmers is

Medium

View Solution

$A$ lot of $100$ bulbs contains $10$ defective bulbs. Five bulbs are selected at random from the lot and are sent to a retail store. Then the probability that the store will receive at most one defective bulb is

EasyMHT CET 2023

View Solution

Let $X \sim B(n, p)$ with mean $\mu$ and variance $\sigma^2$. If $\mu=2 \sigma^2$ and $\mu+\sigma^2=3$,then $P(X \leq 3)=$

EasyTS EAMCET 2020

View Solution

$A$ person buys a lottery ticket in $50$ lotteries,in each of which his chance of winning a prize is $\frac{1}{100}$. What is the probability that he will win a prize at least once?

Medium

View Solution

For a binomial variate $X \sim B(n, p)$,the difference between the mean and variance is $1$ and the difference between their squares is $11$. If the probability $P(X=2) = m\left(\frac{5}{6}\right)^n$ and $n=36$,then $m : n =$

DifficultAP EAMCET 2024

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

The probability mass function of a random variable $X$ is given by $P(X = x) = \frac{^5C_x}{2^5}$, for $x = 0, 1, 2, 3, 4, 5$ and $0$ otherwise. Which of the following is correct?

Similar Questions

The probability that a student is not a swimmer is $\frac{1}{5}$. Then the probability that out of five students,four are swimmers is

$A$ lot of $100$ bulbs contains $10$ defective bulbs. Five bulbs are selected at random from the lot and are sent to a retail store. Then the probability that the store will receive at most one defective bulb is

Let $X \sim B(n, p)$ with mean $\mu$ and variance $\sigma^2$. If $\mu=2 \sigma^2$ and $\mu+\sigma^2=3$,then $P(X \leq 3)=$

$A$ person buys a lottery ticket in $50$ lotteries,in each of which his chance of winning a prize is $\frac{1}{100}$. What is the probability that he will win a prize at least once?

For a binomial variate $X \sim B(n, p)$,the difference between the mean and variance is $1$ and the difference between their squares is $11$. If the probability $P(X=2) = m\left(\frac{5}{6}\right)^n$ and $n=36$,then $m : n =$

Vedclass Test Series

Exam Paper Generator

Online Exam Module