Supplementary Exercises on Probability
Chapter 2, BSNS2120, J. Wang
P(A) and P(B) denote the probability of event A and event B, respectively.
X and Y are random variables. E(X) = expected value of X. 2 = variance.
1. 0P(A)1.
a. True
b. False
2. P(A) tells the _________ that event A may occur.
a. profit
b. chance
c. cost
d. average
3. If P(A)=0, then it means that event A
a. will never happen
c. will possibly happen sometime
b. will happen for sure
4. If P(A)=1, then it means that event A
a. will never happen.
c. will possibly happen sometime.
b. will happen for sure.
5. If the probability of “Event A occurs” is 0.6, then the probability of “Event A does not occur”
is
a. 0.4
b. 0.6
c. 0.5
d. 0
e. 1
6. Let event A be the result of tossing a coin for the first time. Let event B be the result of
tossing the coin for the second time. Event A and event B are __________ events.
a. mutually exclusive
b. dependent
c. independent
7. Let P(A|B) denote the probability of A given event B occurs. If A and B are independent
events, then
a. P(A|B)=P(A)
b. P(A|B)=P(B)
8. If A and B are independent events, then the joint probability P(AB)=P(A and B) is calculated
as
a. P(A)+P(B)
b. P(A)*P(B)
c. P(A|B)*P(A)
9. There are two (2) green chips and two (2) red chips in a bag. Suppose you take one chip
randomly from the bag. What is the probability you have a green chip?
10. There are two (2) green chips and two (2) red chips in a bag. Suppose you take one chip
randomly from the bag, and it is red. You do not put the red chip back to the bag (i.e., no
replacement); and take a chip randomly again from the chips remaining in the bag.
What is the probability that the second chip is green?
11. There are two (2) green chips and two (2) red chips in a bag. Suppose you take one chip
randomly from the bag, and it is red. You put the red chip back to the bag (i.e., with
replacement); and then take a chip randomly again from the bag.
What is the probability that the second chip is green?
1
12. If there are only two possible outcomes, A and B, for an action, then what is the value of
P(A)+P(B) ?
a. 0
b. 0.5
c. 1
d. 100
13. The expected value of a random variable X cannot be more than 1 (i.e., E(X)1).
a. True
b. False
14. The expected value of a random variable X cannot be negative (i.e., E(X)0).
a. True
b. False
15. The variance of a random variable X cannot be negative (i.e., 20).
a. True
b. False
16. The variance of a random variable X cannot be more than 1 (i.e., 21).
a. True
b. False
17. If variance 2=0, then it means that
a. X’s value is not random so that X can take only one value.
b. X is a very dispersed random variable.
c. 2=0 does not make sense.
18. The _______ the variance, the more dispersed the possible values of X.
a. larger
b. smaller
19. We must calculate the expected value before calculating the variance.
a. True
b. False
20. We must calculate the variance first in order to calculate the standard deviation.
a. True
b. False
21. What information is given in the distribution of a random variable?
a. The variable’s probability.
b. The values of expected value and variance.
c. All possible outcomes and their probabilities.
d. Only the possible outcome that is most likely to occur.
n
22. In the formula for E(X), E ( X )   X i P( X i ) , Xi means _____________.
i 1
a. number of possible values of X
b. the i-th possible value of X
c. probability of the i-th possible value of X
n
23. In the formula for E(X), E ( X )   X i P( X i ) , n means _____________.
i 1
a. the largest possible value that X can take
b. a possible value that X can take
c. number of possible values that X can take
d. number of expected values X may have
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For Questions 24, 25, and 26:
Suppose X’s distribution is as follows:
Possible values of X
Probability
0
0.6
1
0.4
-------------------------------------------------24. The expected value of X is _________.
a. 1
b. 0.6
c. 0.5
d. 0.4
e. 0.3
25. The variance of X must be _________.
a. less than 0
b. equal to 0
d. None of above.
c. greater than 0
26. The standard deviation must be __________.
a. less than 0
b. equal to 0
d. None of above.
c. greater than 0
f. 0
27. Variance is used to measure the _________ of a probability distribution.
a. dispersion
b. mean
c. median
28. A distribution of a random variable can have __________________ expected value(s).
a. only one
b. many
c. one or many
29. A distribution of a random variable can have __________________ variance(s).
a. only one
b. many
c. one or many
30. If a random variable X’s variance is 0, then it means ____________.
a. X’s expected value is 0
b. X takes some value always
c. X takes value 0 always
d. None of above. It does not make sense.
31. If random variable X’s expected value is 0, then it means ___________.
a. X takes one value which is 0
b. average value of X is 0
c. variance of X is 0
d. probability of X is 0
e. None of above. It does not make sense.
32. If random variable X’s expected value is negative, then it means ___________.
a. all possible values of X are negative
b. all possible values of X are positive
c. some possible values of X are negative
33. Probability for a day having rain in Seattle during spring is 0.64. If in a day of spring there is
rain in New York, what is the probability that Seattle also has rain either?
a. 0.64
b. Greater than 0.64.
c. Less than 0.64.
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For Problems 34-37:
Probabilities of having a flat tire and a dead engine are 0.06 and 0.02 respectively.
34. What is the probability that an engine works?
35. The chance to have a dead engine at the time when we have a flat tire is ______________.
36. The chance that we have a flat tire and dead engine at same time is _____________.
37. The probability that both tire and engine work normally is ______________.
For Question 38 - 40:
Suppose X’s distribution is as follows:
Possible values of X
Probability
$10
0.5
-$6
0.5
38 . Expected value E(X) is _________.
a. -$6
b. -$3
c. 0
f. $5
g. $10
d. $1
e. $2
39. If John plays this game for 100 times, how much he will win or lose from this 100-times
play?
40. If John plays this game for 100 times, how much on average he could expect to win or lose
from this 100-times play?
41. A Normal distribution has two parameters. They are
a. X and E(X)
b.  and 
42. The parameter  in the Normal distribution represents the
a. mean.
b. expected value
c. Both a and b.
43. In a Normal distribution,  can be negative.
a. True
b. False
44. In a Standardized Normal distribution, =______ and =_______.
a. 0, 1
b. 1, 0
c. 0, 0
d. 1, 1
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Answer:
1.a
2.b
11. 1/2
12.c
21.c
22.b
31.b
32.c
39.Do not know
3.a
13.b
23.c
33.a
40.$200
4.b
14.b
24.d
34.0.98
41.b
5.a
15.a
25.c
35.0.02
42.c
6.c
7.a
16.b
17.a
26.c
27.a
36.0.0012
43.a
44.a
8.b
9. 1/2
18.a
19.a
28.a
29.a
37. 0.9212
10. 2/3
20.a
30.b
38.e
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