Embibe Experts Solutions for Chapter: Probability, Exercise 1: NDA & NA EE 2019 Paper 1 Mathematics

Consider a random variable $X$ which follows Binomial distribution with parameters $n=10$ and $p=\frac{1}{5}.$ Then, $Y=10-X$ follows Binomial distribution with parameters $n$ and $p$ respectively given by

If $A$ and $B$ are two events such that $P\left(A\right)=0.6, P\left(B\right)=0.5$ and $P(A\cap B)=0.4,$ then consider the following statements

1. $P(\overline{A}\cup B)=0.9$

2. $P(\overline{B}/\overline{A})=0.6$

Which of the above statements is/are correct?

Three cooks $X, Y$ and $Z$ bake a special kind of cake and with respective probabilities $0.02, 0.03$ and $0.05,$ it fails to rise. In the restaurant where they work, $X$ bakes $50\%, Y$ bakes $30\%$ and $Z$ bakes $20\%$ of cakes. What is the proportion of failures caused by $X?$

Two dice are thrown simultaneously. What is the probability that the sum of the numbers appearing on them is a prime number?

If $5$ of a Company's $10$ delivery trucks do not meet emission standards and $3$ of them are chosen for inspection, then what is the probability that none of the trucks chosen will meet emission standards?

There are $3$ coins in a box. One is a two-headed coin; another is a fair coin; and third is biased coin that comes up heads $75\%$ of time. When one of the three coins is selected at random and flipped, it shows heads. What is the probability that it was the two-headed coin? $?$

Consider the following statements:

$1.$ If $A$ and $B$ are mutually exclusive events, then it is possible that $P\left(A\right)=P\left(B\right)=0.6$

$2.$ If $A$ and $B$ are any two events such that $P\left(\frac{A}{B}\right)=1,$ then $P\left(\frac{\overline{B}}{\overline{A}}\right)=1$

Which of the above statement is/are correct?

If a fair die is rolled $4$ times, then what is the probability that there are exactly $2$ sixes?