Embibe Experts Solutions for Exercise 1: Exercise

Two cards were drawn without replacement from a well-shuffled pack of $52$ cards. Find the probability distribution of the number of cards of honour (i.e. Jack, Queen, King and Ace).

A random variable $X$ has the following probability distribution :

Find the value of $C$ and also calculate the mean of the distribution.

Following is the distribution function F (x) of a discrete r.v. X

$\begin{array}{|lllllll|}\hline x& 1& 2& 3& 4& 5& 6\\ \mathrm{F}\left(x\right)& 0.2& 0.37& 0.48& 0.62& 0.85& 1\\ \hline\end{array}$

Find $P(X\le 3), P(2<X<5).$

Two biased dice are thrown together. For the first die $\mathrm{P}\left(6\right)=\frac{1}{2},$ the other scores being equally likely while for the second die, $\mathrm{P}\left(1\right)=\frac{2}{5}$ and the other scores are equally likely. Find the probability distribution of " the number of ones seen ".

The range of a random variable $X$ is $\{1,2,3,\dots .\}$ and $P(X=k)=\frac{c^k}{k!}$, $(k=1,2,3,\dots )$. Find the value of $c$ and $P(0<X<3)$.

Suppose that $80\%$ of all families own a television set. If $10$ families are interviewed at random, find the probability that seven families own a television set.

The probability that a person picked at random will support a constitutional amendment requiring an annual balanced budget is $0.8$. If nine individuals are interviewed and they respond independently, what is the probability that at least two-thirds of them will support the amendment

One in $9$ ships is likely to be wrecked, when they are set on sail, when $6$ ships are on sail find the probability for exactly three will arrive safely.