Embibe Experts Solutions for Chapter: Binomial Distribution, Exercise 1: MHT-CET 2017

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

The probability that a person wins a prize on a lottery ticket is $\frac{1}{4}.$ If he purchases $5$ lottery tickets at random, then the probability that he wins at least one prize is

In a binomial distribution, mean is $18$ and variance is $12$ then probability of success $\left(p\right)=....$

A die is thrown four times. The probability of getting perfect square in at least one throw is

A random variable $X\backsim B(n, p).$ If values of mean and variance of $X$ are $18$ and $12$ respectively then total number of possible values of $X$ are

For the following distribution function $F\left(x\right)$ of a random variable $X$

$P \left(3<X \le 5\right)=$

The p. d. f. of a random variable $x$ is given by $f\left(x\right)=\left\{\begin{array}{ll}\frac{1}{4a},\left(a>0\right)& 0<x<4a,\\ 0,& \text{Otherwise}\end{array}\right.$ and $P\left(x<\frac{3a}{2}\right)=kP\left(x>\frac{5a}{2}\right)$ then$k=\dots \dots$.