Embibe Experts Solutions for Chapter: Probability, Exercise 2: Level 2

The chance of one event happening is the square of the chance a $2^{\mathrm{nd}}$ event, but odds against the first are the cubes of the odds against the $2^{\mathrm{nd}}$. Chances of each (Assume that both events are neither sure nor impossible) are $\frac{1}{x}$ and $\frac{1}{y}$, then $\left(x+y\right)$ is

The odds that a book will be favourably reviewed by three independent critics are $5$ to $2, 4$ to $3$ and $3$ to $4$ respectively. If the probability that of the three reviews a majority will be favourable is $\frac{209}{a}$, then a is

For any two events $A$ and $B,$ which one of the following holds?

A coin is tossed until a head appears or it has been tossed thrice. Given that head doesn't appear on the first toss, the probability that coin tossed thrice is

In a bolt factory, machines $X,Y,Z$ manufacture bolts that are respectively $25\%,35\%$ and $40\%$ of the factory's total output. The machines $X,Y,Z$ respectively produce $2\%,4\%$ and $5\%$ defective bolts. A bolt is drawn at random from the product and is found to be defective. What is the probability that it was manufactured by machine $X$ ?

An ordinary die is rolled in a certain number of times. The probability of getting an odd number $2$ times is equal to the probability of getting an even number $3$ times. Then, the probability of getting an odd number on an odd number of times, is

If $X$ follows a binomial distribution with parameters $n=100$ and $p=\frac{1}{3},$ then $P(X=r)$ is maximum when

A certain type of missile hits the target with a probability $p=0.3.$ What is the least number of missiles should be fired so that there is at least $80\%$ probability that the target is hit?