D.P. GUPTA, Preetima Bajpai and, Sanjeev Kumar Jha Solutions for Chapter: Probability, Exercise 1: Exercise 1

If a certain missile will hit the target one out of four times and four such missiles are fired at the same time, then what is the probability that the target will be hit atleast once?

The probability that at least one of $A$ and $B$ occurs is $0.6.$ If $A$ and $B$ occur simultaneously with probability $0.3$, then find the probability of non-occurrence of  $A+$ Probability of non-occurrence of $B$.

If $P\left(A\cup B\right)=\frac{2}{3}, P\left(A\cap B\right)=\frac{1}{6}$ and $P\left(A\right)=\frac{1}{3}$ then

If $A$ and $B$ are two events, then which is not correct

The probability of India winning a test match against Australia is $\frac{1}{2}$ assuming independence from match to match. The probability that in a match series India's second win occurs at third test match is

According to the label, a regular can of Campbell's ${}^{\mathrm{TM}}$ soup holds an average of $305 \mathrm{gm}$ with a standard deviation of $4.2 \mathrm{gm}$. Then the probability that a can will be sold that holds more than $306 \mathrm{gm}$ is

If $F\left(x\right)=\frac{1}{\mathrm{\pi }}\left(\frac{\mathrm{\pi }}{2}+{\tan }^{-1}\right)-\infty <x<\infty$ is a distribution function of a continuous variable $X,$ then $P\left(0\mathit{\le }x\mathit{\le }1\right)$ is

A box contains $20$ identical balls of which $10$ are blue and $10$ are green. The balls are drawn at random from the box one at a time with replacement. The probability that a blue ball is drawn $4^{\mathrm{th}}$ time on the $7^{\mathrm{th}}$ draw is