Maharashtra Board Solutions for Chapter: Binomial Distribution, Exercise 2: MISCELLANEOUS EXERCISE 8

A computer installation has $10$ terminals. Independently, the probability that any one terminal will require attention during a week is $0.1$. Find the probabilities that $3$ or more terminals will require attention during the next week.

In a large school, $80\%$ of the pupils like mathematics. A visitor to the school asks each of $4$ pupils, chosen at random, whether they like mathematics. Calculate the probabilities of obtaining an answer yes from $0,1,2,3,4$ of the pupils.

In a large school, $80\%$ of the pupils like mathematics. A visitor to the school asks each of $4$ pupils, chosen at random, whether they like mathematics. Find the probability that the visitor obtains the answer yes from at least $2$ pupils when the number of pupils questioned remains at $4$.

In a large school, $80\%$ of the pupils like mathematics. A visitor to the school asks each of $4$ pupils, chosen at random, whether they like mathematics. Find the probability that the visitor obtains the answer yes from at least $2$ pupils when the number of pupils questioned is increased to $8$.

It is observed that, it rains on $12$ days out of $30$ days. Find the probability that it rains exactly $3$ days of week.

It is observed that, it rains on $12$ days out of $30$ days. Find the probability that it will rain on at least $2$ days of given week.

If probability of success in a single trial is $0.01$. How many trials are required in order to have probability greater than $0.5$ of getting at least one success?

In binomial distribution with five Bernoulli's trials, probability of one and two success are $0.4096$ and $0.2048$ respectively. Find probability of success.