1. The probabilities that three men hit a target are respectively 1/6, 1/4 and 1/3. Each man shoots once at the target. What is the probability that exactly one of them hits the target?

• 31/72

2. A problem in mathematics is given to three students whose chances of solving it are 1/3, 1/4, 1/5. What is the probability that the problem will be solved?

• 0.6

3. You are given P[A∪B] = 0.7 and P[A∪B^c] = 0.9 . Determine P[A] .

• 0.6

4. An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44 . Calculate the number of blue balls in the second urn.

• 4

5. The probability that a boy will not pass an examination is 3/5 and that a girl will not pass is 4/5. Calculate the probability that at least one of them passes the examination.

• 13/25

6. A bag contains 5 red discs and 4 blue discs. If 3 discs are drawn from the bag without replacement, find the probability that all three are blue.

• 1/21

7. Find the variance for the given probability distribution.

X	0	2	4	6
P(x)	0.05	0.17	0.43	0.35

• 2.8544

8. A bag contains 5 white, 7 red and 8 black balls. Four balls are drawn one by one with replacement, what is the probability that at least one is white?

• 

9. Формулой Бернулли называется формула

• 

10. Indicate the formula of computing variance of a random variable X with expectation µ.

• 

11. How would it change the variance of a random variable X if we add a number to the X?

• Var(X+a)=Var(X)

12. How would it change the expected value of a random variable X if we multiply the X by a number k.

• 

13. Which of the following expressions indicates the occurrence of exactly one of the events A, B, C?

• 

14. Which of the following expressions indicates the occurrence of at least one of the events A, B, C?

• 

15. Which of the following expressions indicates the occurrence of all three events A, B, C simultaneously?

• 

16. Which of the following expressions indicates the occurrence of exactly two of events A, B, C?

• 

17. Conditional probability P(A|B) can be defined by

• 

18. Urn I contains a white and b black balls, whereas urn II contains c white and d black balls. If a ball is randomly selected from each urn, what is the probability that the balls will be both black?

• 

19. The table below shows the probability mass function of a random variable X.

xi	0	x2	5
pi	0.1	0.2	0.7

If E[X]=5,5 find the value of x₂.

• 10

20. The probability of machine failure in one working day is equal to 0.01. What is the probability that the machine will work without failure for 5 days in a row.

• 0.95099

21. The cumulative distribution function of a discrete random variable X is given by Find P{3<X<9}.

• 0,6

22. A fair die is rolled three times. A random variable X denotes the number of occurrences of 6’s. What is the probability that X will have the value which is not equal to 0.

• 91/216

23. Find the expectation of a random variable X if the cdf .

• 5

24. Compute the mean for continuous random variable X with probability density function .

• 1/3

25. If the variance of a random variable X is given Var(X)=3. Then Var(2X) is

• 12

26. Indicate the expectation of a Poisson random variable X with parameter .

• 

27. Indicate the variance of a Poisson random variable X with parameter .

• 

28. Indicate the formula for conditional expectation.

• 

29. The table below shows the pmf of a random variable X. What is the Var(X)?

X	-2	1	2
Р	0,1	0,6	0,3

• 1.2

30. The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function . Calculate the probability that the lifetime of the machine part is less than 6.

• 0.47

31. The lifetime of a machine part has a continuous distribution on the interval (0, 40) with probability density function . Calculate the probability that the lifetime of the machine part is less than 5.

• 0.42

32. If Var(X)=2, find Var(-3X+4).

• 18

33. The table below shows the pmf of a random variable X. Find E[X] and Var(X).

X	-1	0	1
P	0.2	0.3	0.5

• E[X]= 0,3; Var(X) =0.61

34. What kind of distribution is given by the density function ()?

• Normal distribution