Embibe Experts Solutions for Chapter: Probability, Exercise 1: BITSAT 2017

A die is thrown $7$ times. What is the probability that an even number turns up at least $4$ times?

Three numbers are chosen at random without replacement from $\{1,2,3,\dots \dots ,8\}$. The probability that their minimum is $3$, given that their maximum is $6$, is

Cards are drawn one by one at random from a well shuffled pack of $52$ cards until $2$ aces are obtained for the first time. The probability that $18$ draws are required for this is

The sum of mean and variance of a Binomial distribution $\left(\overrightarrow{BD}\right)$ for $3$ trials is $2.7$, then the binomial distribution $\overrightarrow{BD}$ is given by

Let $A$ and $B$ are two independent events. If the probability that both $A$ and $B$ occur together is $\frac{1}{6}$ and the probability that neither of them occurs is $\frac{1}{3}$, then the probability of occurrence of $A$ is

In a test an examiner either guesses or copies or knows the answer to a multiple choice question with $4$ choices. The probability that he/she makes a guess is $\frac{1}{3}$. The probability that he/she copies the answer is $\frac{1}{6}$. If the probability that the answer is correct, given that he/she copied it is $\frac{1}{8}$, then the probability that he/she knows the answer to a question given that he/she correctly answered it, is

If the papers of $4$ students can be checked by any one of the $7$ teachers, then the probability that all the $4$ papers are checked by exactly $2$ teachers, is equal to

A coin is tossed $7$ times. Each time a man calls head. The probability that he wins the toss at least four times is