Embibe Experts Solutions for Chapter: Probability, Exercise 1: JEE Main - 10th April 2019 Shift 1

There rotten apples are mixed accidently with seven good apples and four apples are drawn one by one without replacement. Let the random variable X denote the number of rotten apples. If $\mu$ and ${\sigma }^2$ represent mean and variance of X, respectively, then $10\left({\mu }^2+{\sigma }^2\right)$ is equal to

Let $S=\left\{w_1,w_2,\dots .\right\}$ be the sample space associated to a random experiment. Let $P\left(w_n\right)=\frac{P\left(w_{n-1}\right)}{2}, n\ge 2$. Let $A=\left\{2k+3l; k, l\in \mathbb{N}\right\}$ and $B=\left\{w_n; n\in A\right\}$. Then $P\left(B\right)$ is equal to

If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces is thrown five times, then the probability that the product of the outcomes is positive, is :

A bag contains six balls of different colours. Two balls are drawn in succession with replacement. The probability that both the balls are of the same colour is $p$. Next four balls are drawn in succession with replacement and the probability that exactly three balls are of the same colours is $q$. If $p: q=m$ $:n$, where $m$ and $n$ are co-prime, then $m+n$ is equal to

A bag contains $6$ balls. Two balls are drawn from it at random and both are found to be black. The probability that the bag contains at least $5$ black balls is

Let $A$ be the event that the absolute difference between two randomly chosen real numbers in the sample space $\left[0,60\right]$ is less than or equal to $a$. If $P\left(A\right)=\frac{11}{36}$, then a is equal to _____ .

In a binomial distribution $\mathrm{B}(n,p)$, the sum and product of the mean & variance are $5$ and $6$ respectively, then find $6(n+p-q)$ is equal to :-

Two dice are thrown independently. Let $A$ be the event that the number appeared on the $1^{\text{st }}$ die is less than the number appeared on the $2^{\text{nd }}$ die, $B$ be the event that the number appeared on the $1^{\text{st }}$ die is even and that on the second die is odd, and $C$ be the event that the number appeared on the $1^{\text{st }}$ die is odd and that on the $2^{\text{nd }}$ is even. Then