Amit M Agarwal Solutions for Chapter: Fundamentals of Probability, Exercise 3: Work Book Exercise 21.3

Given $P\left(A\right)=\frac{3}{5}$ and $P\left(B\right)=\frac{1}{5}.$ Find $P\left(A \mathrm{or} B\right)$, if $A$ and $B$ are mutually exclusive events.

If $E$ and $F$ are events such that $P\left(E\right)=\frac{1}{4},P\left(F\right)=\frac{1}{2}$ and $P\left(E \mathrm{and} F\right)=\frac{1}{8}$. Find: $\left(\mathrm{i}\right)$ $P\left(E \mathrm{or} F\right)$ $\left(\mathrm{ii}\right)$ $P \left(\mathrm{not} E \mathrm{and} \mathrm{not} F\right)$.

An experiment yields $3$ mutually exclusive and exhaustive events $A,B$ and $C$. If $P\left(A\right)=2 P\left(B\right)=3 P\left(C\right)$, then $P\left(A\right)$ is equal to

$A$ and $B$ are two events where $P\left(A\right)=0.25$ and $P\left(B\right)=0.5$. The probability of both happening together is $0.14$. The probability of both $A$ and $B$ not happening is

Let $A$ and $B$ be two independent events such that $P\left(A\right)=\frac{1}{5},P\left(A\cup B\right)=\frac{7}{10}.$ Then, $P\left(\overline{B}\right)$ is equal to

$A,B$ and $C$ are the events such that $P\left(A\right)=0.3, P\left(B\right)=0.4, P\left(C\right)=0.8, P\left(A\cap B\right)=0.08$, $P\left(A\cap C\right)=0.28, P\left(A\cap B\cap C\right)=0.09$. If $P\left(A\cup B\cup C\right)\ge 0.75$, then $P\left(B\cap C\right)$ lies in the interval

A die is rolled so that the probability of face $i$ is proportional to $i,i=1,2,\dots ,6$. The probability of an even number occurring when the die is rolled, is