This document contains 4 probability questions with solutions. Question 1 asks for the probability of rolling a number between 2 and 4 on a standard 6-sided die. Question 2 asks for the correct notation to represent the probability of getting 2 or fewer heads in 3 coin tosses. Question 3 asks to calculate the expected number of heads when tossing 2 coins. Question 4 asks to evaluate the expected value of winning or losing money based on rolling a single 6-sided die. The solutions provided are A, D, B, and B respectively.

1. Question 1:
Suppose a fair, six-sided die is rolled. Let X be the number on the side of the die facing up.
What is the probability that X is at least two, but less than 5?
A. 2/3
B. 4
C. 3
D. 1/2
Question 2:
Let X be the number of heads found in 3 tosses of a coin. Which ONE of the choices below is
the correct notation for the probability that X is at most 2?
A. P(X>2)
B. P(X?2)
C. P(X?2)
D. P(X<2)
Question 3:
Two coins are tossed. The sample space, S, is given by S = {HH, HT, TH, TT}. Let X be the
number of heads attained in the two tosses. Find E(X).
A. 1.5
B. 2
C. 0.5
D 1
Question 4:
You are playing a game of chance, based on the outcome of a roll of a single, fair, six-sided die.
If you roll a 1, 2, or 3, you will win $12. If you roll a 4, you will win $6. If you roll a 5 or 6, you
will lose $18. Let X be the amount of money you win in a single play of this game (i.e. a single
roll). Evaluate ?X.

2. A. $ 13/6 (i.e. about $2.17)
B. $0
C. $1
D. 3.5
Solution
Question 1: Suppose a fair, six-sided die is rolled. Let X be the number on the side
of the die facing up. What is the probability that X is at least two, but less than 5? A. 2/3
Question 2: Let X be the number of heads found in 3 tosses of a coin. Which ONE of the choices
below is the correct notation for the probability that X is at most 2? D. P(X<2) Question 3:
Two coins are tossed. The sample space, S, is given by S = {HH, HT, TH, TT}. Let X be the
number of heads attained in the two tosses. Find E(X). B. 2 Question 4: You are playing a
game of chance, based on the outcome of a roll of a single, fair, six-sided die. If you roll a 1, 2,
or 3, you will win $12. If you roll a 4, you will win $6. If you roll a 5 or 6, you will lose $18. Let
X be the amount of money you win in a single play of this game (i.e. a single roll). Evaluate ?X.
B. $0