Parthasarathi Mukhopadhyay and Manabendra Nath Mukherjee Solutions for Exercise 5: EXERCISE

A coin is tossed $999$ times. If $X$ is the number of times head appeared, then $P\left(X=r\right)$ if maximum when $r=$

Find the probability distribution of multiples of three in five tosses of a die.

In five throws with a pair of dice, what is the probability of throwing doublets at least thrice?

An unbiased coin is tossed $6$ times. Find using the binomial distribution, the probability of getting at least five heads.

A coin is biased so that the head is $3$ times as likely to occur as tail. If the coin is tossed $6$ times, find the probability distribution of tails.

Find the probability distribution of the number of sixes in three tosses of a die.

The probability that a student is not a swimmer is $\frac{1}{3}$. What is the probability that out of $6$ students exactly $2$ are swimmer?

(Write answer in simplest fraction form)

The probability that an event $A$ occurs in a single trial of an experiment is $0.2$. Four independent trials of the experiment are performed. What is the probability that $A$ occurs at least once?

(Write answer in decimal form)