Embibe Experts Solutions for Chapter: Probability, Exercise 1: CUSAT CAT 2017

A coin is tossed five times. If the outcomes are $2$ heads and $3$ tails (in some order), then what is the possibility that the fourth toss is a head?

The probability that event $A$ occur is $\frac{3}{4}$ and the probability the $B$ occur is $\frac{2}{3}$. Minimum and maximum possible values of $P\left(A\cap B\right)$ is

One ticket is selected at random from $50$ tickets numbered $00,01,02,....,49$. Then, the probability that the sum of the digits on the selected ticket is $8$, given that the product of these digits is zero, equals

All the thirteen spade cards are drawn from a pack and formed a new pack. From these $13$ spade cards, cards are drawn one by one without replacementd till the ace of spade comes. The probability the ace comes in the fourth draw is

A problem in mathematics is given to three students$A, B, C$ and their respective probability of solving the problem is $\frac{1}{2},\frac{1}{3}$ and $\frac{1}{4}$, the probability that the problem will be solved is

Geetha and Somu appear for an interview for two vacancies in a company. The probability of Geethas selection is $\frac{1}{5}$ and Somu is $\frac{1}{6}$. Then the probability that

(i) both of them are selected (ii) both of them are not selected are respectively