probability and statistics 2

In the box set of 10 red and 5 blue buttons. Removed two buttons at random. What is the probability of selected buttons are same color?

• 11/21

• 21/11

• 3/11

• 11/17

• 17/21

Three teachers take an exam in a group of 30 people, the first teacher selects 6 students, the second teacher selects 3 students and the third 21 students. The chances of that students pass the examinations at the first teacher is equal to 40%, at the second 10% , and third 70%.Find the probability of randomly selected student will pass the exam.

• 0.48

• 0.58

• 0.68

• 0.78

• 0.88

The density function of X continuous random variables is f(x)=3x+1, in (1/5,1/2), in out if interval f(x)=0. Find expected value of X random variables.

• 0.111

• 0.202

• 0.222

• 0.101

• 0.2

Suppose X continuous random variables and Var(X)=0.004. Evaluate the probability of ІX-E(x)І<0.2 event by Chebyshev inequality.

• 0.6

• 0.7

• 0.8

• 0.9

• 0.5

The distribution law of X discrete random variables are like this. x1=1 , x2=3 and p1=0.4 , p2=0.6.Using the Chebyshev’s inequality evaluate occurrence of ІX-E(x)І≥4 event.

• 0.06

• 0.07

• 0.08

• 0.09

• 0.1

The barber shop serves on average 180 person in a day. What is the probability of to serve at least 210 person a day in a particular time.

• 4/7

• 5/7

• 6/7

• 3/7

• 2/7

The distribution function of X continuous random variables is f(x)= cx+2, in (0, 1/5). Then find constant number of c.

• 10

• 15

• 20

• 25

• 30

Coin tossed three times. Find the probability that head falls at most one time.

• 1/2

• 1/3

• 1/4

• 1/5

• 1/6

The distribution function of X continuous random variables is f(x)= cx/3+2/3, in (0, 1/3). Then find constant number of c.

• 22

• 32

• 42

• 52

• 62

There are 10 elements in device. During the time of T the probability of out of order the element is equal to 0.05. Using the Chebyshev inequality find the probability of subtraction of number of out of order elements and expected value are less than two.

• $\approx0.88$

• $\approx0.68$

• $\approx0.58$

• $\approx0.48$

• $\approx0.38$