Embibe Experts Solutions for Chapter: Probability, Exercise 1: AMU-AT (B.Tech.) 2017

Two persons $A$ and $B$ take turns in throwing a pair of dice. The first person to throw $9$ from both dice will be awarded the price. If $A$ throws first, then the probability that $B$ wins

The probability that in a year of the $22 \mathrm{nd}$ century chosen at random, then there will be $53$ Sundays, is

If four whole numbers taken at random are multiplied together, then the probability that the last digit in the product is $1,3,7,$ or $9,$ is

If $A_i(i=1,2,\dots ,n)$ are $n$ independent events, with $P\left(A_i\right)=1-\frac{1}{2^i}$, then the probability that atleast one of the $n$ events occurs, is

Let $A$ be an event that a family has children of both sexes and $B$ be the event that the family has atmost one boy. If the family has $3$ children then the events $A$ and $B$ are

A fair coin is tossed $n$ times. Let the random variable $X$ denote the number of times the head occurs. If $P[X=1], P[X=2]$ and $P[X=3]$ are in arithmetic progression (AP), then the number $n$ of independent trial is

If $A$ and $B$ are two events associated to some experiment $E$ such that $P\left(A\right)=0.5, P\left(B\right)=0.4,$ $P(A\cap B)=0.3,$ then $P\left(\frac{A^C}{B^C}\right)$ is equal to

If $X$ follows a binomial distribution with parameters $n=100,p=\frac{1}{3},$ then $P\left(X=r\right)$ is maximum, when $r$ is equal to