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

If $A$ and $B$ are the events such that $P\left(A\right)=\frac{1}{2}, P\left(B\right)=\frac{1}{3} \text{and} P\left(A\cap B\right)=\frac{1}{4}$, then find $P\left(\frac{A}{B}\right)$.

If $A$ and $B$ are the events such that $P\left(A\right)=\frac{1}{2}, P\left(B\right)=\frac{1}{3} \text{and} P\left(A\cap B\right)=\frac{1}{4}$, then find $P\left(\frac{B}{A}\right)$.

A family has two children. What is the probability that both children are boys, given that at least one of them is a boy?

Ten cards numbered $1$ to $10$ are placed in box, mixed up thoroughly and then one card is drawn randomly. If it is known that the number on the drawn card is more than $3$, what is the probability that it is an even number ?

The persons $A, B$ and $C$ shoot to hit a target. Their probabilities of hitting the target are $\frac{5}{6},\frac{4}{5}$ and $\frac{3}{4}$ respectively. Find the probability that at least one person hits the target.

A bag contains $5$ white, $7$ red and $4$ black balls. If four balls are drawn one by one with replacement, what is the probability that none is white?

Bag $A$ contains $4$ white balls and $3$ black balls, while Bag $B$ contains $3$ white balls and $5$ black balls. Two balls are drawn from Bag $A$ and placed in Bag $B$. Then, what is the probability of drawing a white ball from Bag $B$?

Of the students in a college, it is known that $\mathrm{}60\mathrm{\%}\mathrm{}$ reside in hostel and $\mathrm{}40\mathrm{\%}\mathrm{}$ are day scholars (not residing in hostel). Previous year results report that $\mathrm{}30\mathrm{\%}\mathrm{}$ of all students who reside in hostel attain $\mathrm{A}$ grade and $\mathrm{}20\mathrm{\%}\mathrm{}$ of day scholars attain $\mathrm{A}$ grade in their annual examination. At the end of the year, one student is chosen at random from the college and he has an $\mathrm{A}$ grade, what is the probability that the student is hostler?