M L Aggarwal Solutions for Chapter: Probability, Exercise 5: CHAPTER TEST

$A$ and $B$ are two events associated with the same random experiment. If $P\left(A\right)=\frac{1}{4}$, $P\left(B\right)=\frac{2}{5},$ and $P\left(A\cup B\right)=\frac{1}{2}$. Find $P\left(A\cap B\right)$. [Write the answer in fraction in the answer box].

In an essay competition, the odds in favour of the four competitors $A,B,C$ and $D$ are $1:2$, $1:3$, $1:4$, and $1:5$ respectively. Find the probability that one of them wins the competition. [Write the answer in the fraction in the answer box].

The probability of the intersection of two events $A$ and $B$ is always less than or equal to the probability of event $A$.

The probability of an occurrence of event $A$ is $0.7$ and that of occurrence of $B$ is $0.3$ and the probability of occurrence of both is $0.4$.

The probability that the home team will win an upcoming football game is $0.77$, the probability that it will tie the game is $0.08$, and the probability that it will lose the game is _____.

If $e_1$, $e_2$, $e_3$, $e_4$ are four elementary events in a sample space and $P\left(e_1\right)=0.1$, $P\left(e_2\right)=0.5$, and $P\left(e_3\right)=0.1$ then the probability of $e_4$ is _____.

If $A$ and $B$ are two events associated with a random experiment such that $P\left(A\right)=0.3,$ $P\left(B\right)=0.2,$ and $P(A\cap B)=0.1$, then the value of $P(A\cap \overline{B})$ is _____.

The probability of happening an event $A$ is $0.5$ and that of $B$ is $0.3$. If $A$ and $B$ are mutually exclusive events, then the probability of neither $A$ nor $B$ is _____.