Statistics and Probability Answers

What is the probability that two persons A and B sit together if they are placed with 15 other people randomly in a row of 17 chairs?

A dice is thrown. What are the probabilities of the following events: A – 6 points are dropped, B – even number of points is dropped, C – a number of points number of points which are multiples of 3?

Let 2S be the total weight of a set of bobs. Number k is called a mean if it is possible to choose k bobs with the total weight S. What is the greatest possible amount of means in a set of 100 bobs?

45 people came to the meeting. It turned out that any two of them having the same number of friends among the visitors are not familiar with each other. What is the greatest number of pairs of friends could be among the participants of the meeting?

Three brothers visited their sick friend in one day, and in the same day their wives also visited him. No one of the visitors came more than once. Every brother has met both of his brothers’ wives in the house of their sick friend. Prove that at least one of the brothers have also met his wife it that house.

The book of 500 pages contains 50 misprints. Estimate the probability that a randomly selected page contains at least 3 misprints.

In a certain group of people there is 1% of color blind. How big a random sample should be for the probability of presence of at least one color-blind in it was not less than 0.95?

It is known that in average there is 1% of left-handers. Estimate the probability that at least four left-handers will be among:

a) 200 people;
b) 10000 people.

Are there two different characteristic functions that coincide on some interval containing the origin?

How many times should the dice be thrown, so that with the probability 1/2 the amount of dropped points will exceed 100?