Subject Experts Solutions for Chapter: Probability, Exercise 1: Practice Exercise

Consider the following statements

$\mathrm{I}.$ If $A$ and $B$ are exhaustive events, then their union is the sample space,

$\mathrm{II}.$ If $A$ and $B$ are exhaustive events, then their intersection must be an empty event.

Which of the above statement(s) is/are correct?

Which one of the following may be the parameter of a binomial distribution?

In a binomial distribution, the occurrence and the non-occurrence of an event are equally likely and the mean is $6.$ The number of trials required is

It has been found that, if $A$ and $B$ play a game $12$ times, $A$ wins $6$ times, $B$ wins $4$ times and they draw twice. $A$ and $B$ take part in a series of $3$ games. The probability that they win alternately, is

Let $X$ denotes the number of scores which exceed $4$ in $18$ tosses of a symmetrical die. Consider the following statements

$\mathrm{I}.$ The arithmetic mean of $X$ is $6.$

$\mathrm{II}.$ The standard deviation of $X$ is $2.$ Which of the above statement($s$) is/are correct?

Suppose $A$ and $B$ are two events. Event $B$ has occurred and it is known that $P\left(B\right)<1.$ What is $P\left(A/B^{\text{'}}\right)$ equal to?

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

The probability that in a random arrangement of the letters of the word '$\mathrm{UNIVERSITY}$', the two $\mathrm{I}$'s do not come together is