M L Aggarwal Solutions for Chapter: Probability, Exercise 10: EXERCISE

An urn contains $5$ red and $4$ white balls. A ball is drawn at random, its colour is noted and is returned to the urn along with two additional balls of the same colour and then a ball is drawn at random. If a red ball has been drawn in the second draw, then find the probability that a red ball was drawn in the first draw."

There are two biased coins. Coin $1$ turns up heads only $40\%$ of the time while coin $2$ turns up heads $70\%$ of the times.  A coin is picked up. What is the probability that it is of type $1$?
 

There are two biased coins. Coin $1$ turns up heads only $40\%$ of the time while coin $2$ turns up heads 70% of the times. A coin is picked up. It is tossed once and comes up heads. What is the probability that it is of type $1$?

There are two biased coins. Coin $1$ turns up heads only $40\%$  of the time while coin $2$ turns up heads $70\%$ of the times.

A coin is picked up. It is tossed twice and comes up heads. What is the probability that it is of type 1?

Bag I contains $4$ red and $3$ white balls; bag II contains $2$ red and $2$ white balls. Two balls are transferred from bag I to bag II and them two balls are drawn from bag II. If the balls drawn from bag II are one red and one white, then find the probability that $2$ red balls were transferred from bag I to bag II.

In a multiple choice question, there are four alternative answers, of which one or more are correct. A candidate will get marks in the question only if he ticks all the correct answers. The candidate decides to tick answers at random. If he is allowed up to three chances to answer the question, then find the probability that he will get marks in the question.

What is the least number of times a pair of dice must be rolled so that the probability of getting a sum of $12$ at least once shall be more than $\frac{1}{2}$.

Find the mean (or expectation) of a discrete random variable $X$ whose probability function is given by  $f\left(x\right)={\left(\frac{1}{2}\right)}^x$  where $X=1, 2,3,........$