Embibe Experts Solutions for Chapter: Probability, Exercise 1: Exercise

If $A \text{and} B$ are two independent events with $P\left(A\right)=\frac{1}{3}\text{ and }P\left(B\right)=\frac{1}{4}$, then $P\left(B^{\text{'}}\mid A\right)$ is equal to

An event $\mathrm{E}$ of a random experiment has the probability $0.4$ to occur. Three independent performances of this experiment are made. Then the probability that $\mathrm{E}$ occurs at least once is

A green and a white dice are rolled in order. Find the conditional probability of obtaining a sum greater than $8$, given that the green die resulted in $6$. 

A couple has two children. Determine the probability that both the children are boys if it is given that at least one of the children is a boy.

A coin is tossed three times. Find $P\left(A/B\right)$ when

$A=$ at most two tails, $B=$ at least one tail

$A$, $B$, $C$ play a game by throwing a pair of dice in that order. One who throws $8$ wins the game. If $A$ starts the game, find their chances of winning.

Rita and Nita throw a die alternately until one of them gets a $5$ for the first time and wins the game. If Rita throws the die first, determine the respective probabilities for Rita and Nita to win.

$A$ and $B$ toss a coin alternately until one of them gets a head first time wins and wins the toss. If $A$ begins, find the respective probabilities for $A$ and $B$ to win the toss.