Embibe Experts Solutions for Exercise 8: Assignment

A coin is tossed $15$ times, then find the probability that exactly $9$ consecutive heads appears, is

If mean and variance of a binomial distribution are $4$ and $2$ then $P\left(\left|x-4\right|\le 2\right)$ where $x$ is binomial variate is given by

$2$ cards are selected randomly from a pack of $52$ cards. The probability that the first card is a club and second is not a queen, is

If $x$ and $y$ co-ordinates of any point $P$ are chosen randomly from intervals $\left[0,2\right]$ and $\left[0,1\right]$ respectively, then the probability $y\le x^2$ is

One mapping is selected at random from all the mappings of the set $A=\left\{a,e,i,o,u\right\}$ into itself. The probability that the selected one is one to one is given by $\frac{m}{n}$, where $m$ and $n$ are coprime then $\left(m+n\right)$ is equal to

$A$ and $B$ each throw a die. The probability that $A$'s throw is not greater than $B$'s is $\frac{p}{q}$ where $p$ and $q$ are coprime then $p+q$ is equal to

An urn contains $2$ white and $2$ black balls. A ball is drawn at random. If it is white, it is not replaced into urn, otherwise it is replaced along with another ball of the same colour. The process is repeated. If the probability that third ball drawn is black is $\frac{p}{q}$, where $p$ and $q$ are coprime then $p+q$ must be

A biased coin with probability $P, 0<P<1$ of heads is tossed until a head appears for the first time. If the probability that the number of tosses required is even is $\frac{1}{6}$ then, $P=\frac{m}{n}$, where $m$ and $n$ are coprime then $n^m$ is equal to