# Solution 5 problems

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Problem 1. Topic: "The space of elementary events"

Whether these events form a complete group of events space of elementary events described an experiment; if two, then you are equally possible; if not - they are incompatible?

Experiment - throwing two regular coins; Event A - «coat of arms on the first coin" Event B - «coat of arms on the second coin."
Problem 2. Theme: "Properties of probabilities"

The fashion designer, is developing a new collection of clothes for the spring season, creates models in white, black and red colors. The probability that the white color is in fashion spring fashion is estimated at 0.3, Black - 0.2, and the likelihood that there will be fashionable red - 0.15. Assuming that the colors are selected independently of one another, evaluate the probability that a collection of color solution is best to at least one of the selected colors.
Problem 3. Theme: "The formula of total probability and Bayes 'formula'

Among university students 30% of first-year students, 35% of students are enrolled in the second year, and the rest - undergraduates. According to the dean's known that in the first year 20% of students passed the session only on the excellent ratings, the second - 30%, 40% among seniors standouts. Caused by random student proved an excellent student. What is the probability that he - an undergrad?

Record table for the distribution law of the random variable X, build a polygon distribution. Find the numerical characteristics of distribution. Record the distribution function and build her schedule. Answer the question about the likelihood of the event described.

Well-regarded head of receiving at least 70% of correct decisions. Let the bank manager - a good leader, make the right decisions with constant probability 0.75. Such a bank manager will take decisions on four important issues of banking policy. The random variable X - the number of correct decisions taken by the manager. What is the probability that the manager will take at least three good decisions?

Examination number 1
Discipline: "Theory of Probability and Mathematical Statistics"
variant №3 (V = (1032) div100 = 3)

Problem 5. Topic: "Descriptive statistics"

For the following sample data to perform the following processing, explaining the results:
a) Find the sample values \u200b\u200bof the arithmetic mean, mode, median;
b) find the scope of the sampling sample variance, sample standard deviation; to verify that the rules "3sigma";
c) to assess the symmetry of the distribution by the first coefficient of Pearson;
d) Find the upper and lower quartiles sample, explain their meaning;
e) build statistical series and grouped histogram;
e) Find the median and modal intervals to compare the middle of these intervals with the values \u200b\u200bof fashion and the median calculated from the sample.
To perform the calculation and histograms recommended means MathCad, Excel.

The rate of car on a stretch of road, km / h:
41 41 29 15 41 43 42 34 41 30
23 48 50 36 35 46 28 46 50 41
55 27 43 53 48 47 34 35 29 42
30 35 38 41 36 38 45 59 44 43

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