Name: __________________________ Date: _____________
1. A penny is tossed. We observe whether it lands heads up or tails up. Suppose the penny
is a fair coin, i.e., the probability of heads is 1 2 and the probability of tails is 1 2 . What
does this mean?
A) Every occurrence of a head must be balanced by a tail in one of the next two or
three tosses.
B) If the coin is tossed many, many times, the proportion of tosses that land heads will
be approximately 1 2 , and this proportion will tend to get closer and closer to 1 2 as
the number of tosses increases.
C) Regardless of the number of flips, half will be heads and half tails.
D) All of the above.
Use the following to answer questions 2-3:
A standard deck of cards has 52 cards. The cards have one of 2 colors: 26 cards in the deck are
red and 26 are black. The cards have one of 4 denominations: 13 cards are hearts (red), 13 cards
are diamonds (red), 13 cards are clubs (black), and 13 cards are spades (black).
2. Two cards are selected at random and the color is recorded. Which of the following is
the correct sample space S for the set of possible outcomes?
A) S = {red, black}
B) S = {(red, red), (red, black), (black, red), (black, black)}
C) S = {0, 1, 2}
D) S = {red, black, hearts, diamonds, clubs, spades
3. Two cards are selected at random and the denomination is recorded. The event D is
defined as the event that the first card is diamonds and the second card is red. Which of
the following correctly defines event DC?
A) DC = {(diamonds, clubs), (diamonds, spades)}
B) DC = {(hearts, clubs), (hearts, spades)}
C) DC = {(hearts, clubs), (hearts, spades), (spades, clubs), (spades, spades), (clubs,
clubs), (clubs, spades)}
D) None of the above.
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Use the following to answer question 4:
If you draw an M&M candy at random from a bag of the candies, the candy you draw will have
one of six colors. The probability of drawing each color depends on the proportion of each color
among all candies made. Assume the table below gives the probabilities for the color of a
randomly chosen M&M:
Color
Probability
Brown
0.3
Red
0.3
Yellow
?
Green
0.1
Orange
0.1
Blue
0.1
4. What is the probability of not drawing a red candy?
A) 0.3
B) 0.6
C) 0.7
D) 0.9
5. Event A occurs with probability 0.2. Event B occurs with probability 0.8. If A and B
are disjoint (mutually exclusive), then
A) P(A and B) = 0.16
B) P(A or B) = 1.0
C) P(A and B) = 1.0
D) P(A or B) = 0.16
Use the following to answer question 6:
At the end of a production run manufacturing rubber gaskets, items are sampled at random and
inspected to determine if the item is Acceptable (A), or Defective (D). Suppose it is planned to
select two items and determine if each is either A or D.
6. What is the sample space S of the outcomes?
A) S = {A or D}
B) S = {AA, DD}
C) S = {AA, AD, DA, DD}
D) Depends upon the assignment of probability to the outcomes of the sampling.
E) Can't be determined until the sample of two items has been collected.
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Use the following to answer question 7:
Consider the following probability histogram for a discrete random variable X:
7. What is P(X < 3)?
A) 0.10
B) 0.25
C) 0.35
D) 0.65
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8. Suppose X is a continuous random variable taking values between 0 and 2 and having
the probability density function below:
What is P(1 ≤ X ≤ 2)?
A) 0.50
B) 0.33
C) 0.25
D) 0.00
9. Consider the following three scenarios and determine if the random variable described
in each is either discrete or continuous.
I. – The increase in length of life of a cancer patient following chemotherapy.
II. – The volume of gasoline lost due to evaporation during the filling of a gas tank.
III. – The number of cracks that exceed 1.5 centimeters in 10 kilometers of a major
highway.
The random variable in scenarios I, II, and III, respectively, is:
A) Continuous, discrete, discrete.
B) Continuous, continuous, discrete.
C) Continuous, continuous, continuous.
D) Discrete, continuous, discrete.
E) Discrete, discrete, continuous.
10. Consider the following distribution of values for a discrete variable X:
X
0
1
2
3
4
P(X = x)
0.2
U
0.3
0.2
0.4
What value of U will make this a proper probability distribution?
A) 0.1
B) 0.25
C) –0.1
D) 0
E) There is no value for U that will make this a probability distribution of a discrete
random variable.
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Use the following to answer question 11:
Suppose there are three balls in a box. On one of the balls is the number 1, on another is the
number 2, and on the third is the number 3. You select two balls at random and without
replacement from the box and note the two numbers observed. The sample space S consists of
the three equally likely outcomes {(1, 2), (1, 3), (2, 3)} (disregarding order). Let X be the sum of
the two balls selected.
11. Which of the following is the correct distribution for X?
A)
B)
C)
D)
12. A random variable X has mean µ = 9 and a standard deviation σ = 2. The random
variable X is multiplied by the constant 3 to create a new variable Y, i.e., Y = 3X.
What is the variance of Y?
A) 36
B) 12
C) 27
D) 6
E) Unable to determine with the information provided.
Use the following to answer question 13:
Let X be a random variable with mean µX = 25 and σX = 6 and let Y be a random variable with
mean µY = 30 and σY = 4. It is known that X and Y are independent random variables.
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13. Suppose the random variables X and Y are added together to create new random
variable W, i.e., W = X + Y.
What is the standard deviation of W?
A) σW = 7.2
B) σW = 100
C) σW = 10
D) σW = 52
E) σW = Unable to determine with the information provided.
Use the following to answer question 14:
Suppose that A and B are two independent events with P(A) = 0.3 and P(B) = 0.3.
14. What is P(A and B)?
A) 0.09
B) 0.51
C) 0.52
D) 0.60
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Answer Key
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
B
B
D
C
B
C
C
C
B
E
B
A
A
A
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