M L Aggarwal Solutions for Chapter: Probability, Exercise 4: EXERCISE

If $A_1,A_2,....$$A_n$ are mutually exclusive and exhaustive events, then $\underset{i=1}{\overset{n}{\sum P\left(A_i\right)}}$ is 

In a class $\mathrm{XI}$th of a school, $40\%$ students are punctual and $30\%$ students are regular. $10\%$ of the students are both punctual and regular. If a student is selected at random from the class, find the probability that he will be punctual or regular or both. 

In an entrance test that is graded on the basis of two examinations, the probability of a randomly chosen student passing the first examination is $0.8$ and the probability of passing the second examination is $0.7$. The probability of passing at least one of them is $0.95$. What is the probability of passing both?

The probability that a student will pass the final examination in both English and Hindi is $0.5$ and the probability of passing neither is $0.1$ . If the probability of passing the English examination is $0.75$, what is the probability of passing the Hindi examination?

In a certain city, the probability of not reading the morning newspaper by the residents is $\frac{1}{2}$ and that of not reading the evening newspaper is $\frac{2}{5}$. The probability of reading both the newspapers is $\frac{1}{5}$. Find the probability that a resident reads either the morning or evening or both the papers. Justify the statement, "Reading newspaper is good habit".

For a post, three persons A, B and C appear in the interview. The probability of A being selected is twice that of B and the probability of B being selected is thrice that of C. If the post is filled, what the probabilities of A, B and C being selected?

Two cards are drawn at random from a pack of $52$ cards. What is probability that the cards are either both aces or both black cards?

In a group of $20$ boys and $10$ girls, $5$ boys and $3$ girls are honest. If two persons are selected at random from the group, find the probability that either both are girls or both are honest. Should there be gender discrimination?