(D) This is a binomial distribution problem where $n = 5$ and the probability of success $p = 0.2$. The probability of failure is $q = 1 - p = 1 - 0.2

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

(D) This is a binomial distribution problem where $n = 5$ and the probability of success $p = 0.2$. The probability of failure is $q = 1 - p = 1 - 0.2 = 0.8$. We need to find the probability that exactly $x = 4$ patients survive. The formula for binomial probability is $P(X = x) = {}^{n}C_{x} p^{x} q^{n-x}$. Substituting the values: $P(X = 4) = {}^{5}C_{4} (0.2)^{4} (0.8)^{5-4}$. $P(X = 4) = 5 \times (0.0016) \times (0.8)$. $P(X = 4) = 5 \times 0.00128 = 0.0064$.

Class 12 Mathematics Probability Binomial distribution

Medium

The probability that a person who undergoes a certain operation will survive is $0.2$. If $5$ patients undergo similar operations,then the probability that exactly four will survive is

MHT CET 2020 All MHT CET

A
$0.0042$
B
$0.0084$
C
$0.0032$
D
$0.0064$

Explore More

Browse All

Question Bank

All Subjects

Class 12 Questions

Class 12

Mathematics Questions

Chapter

Probability

Subtopic

Binomial distribution

Previous Year

MHT CET 2020 Paper All MHT CET years →

$A$ man takes a step forward with probability $0.4$ and backwards with probability $0.6$. The probability that at the end of eleven steps,he is one step away from the starting point is

MediumMHT CET 2023

View Solution

$A$ pair of fair dice is thrown $4$ times. If getting the same number on both dice is considered as a success,then the probability of exactly two successes is:

MediumMHT CET 2025

View Solution

How many times must a fair coin be tossed so that the probability of getting at least one head is at least $0.8$?

Difficult

View Solution

An experiment succeeds twice as often as it fails. Find the probability that in the next six trials,there will be at least $4$ successes.

Medium

View Solution

If $A$ and $B$ simultaneously toss one coin each,$50$ times,then the probability of not getting a tail on both the coins in any single toss is:

EasyAP EAMCET 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

The probability that a person who undergoes a certain operation will survive is $0.2$. If $5$ patients undergo similar operations,then the probability that exactly four will survive is

Similar Questions

$A$ man takes a step forward with probability $0.4$ and backwards with probability $0.6$. The probability that at the end of eleven steps,he is one step away from the starting point is

$A$ pair of fair dice is thrown $4$ times. If getting the same number on both dice is considered as a success,then the probability of exactly two successes is:

How many times must a fair coin be tossed so that the probability of getting at least one head is at least $0.8$?

An experiment succeeds twice as often as it fails. Find the probability that in the next six trials,there will be at least $4$ successes.

If $A$ and $B$ simultaneously toss one coin each,$50$ times,then the probability of not getting a tail on both the coins in any single toss is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module