OPMT 1197
Business Statistics
Lecture 4: Basic Probability Concepts
1. Determine the following probabilities:
(a) Drawing either an Ace or a Spade from a well-shuffled deck of 52 cards?
(b) Drawing either a Red Ace or a Spade? (c) Drawing neither an Ace nor a Spade?
Solutions: 1. (a) 16/52 (b) 15/52 (c) 36/52
Multiplication Law and Independent Events
1. You flip a coin twice. What is the probability of obtaining heads on both flips?
2. You roll a pair of six-sided dice. Find the probability that both die rolled come up 5’s.
3. You roll one six-sided die. Find the probability of rolling either a 2 or a 5.
4. From its TV studio’s in Bountiful, Reality TV is marketing a new reality TV series called
“Who Wants To Marry a Bigamist”. In the exciting final episode the bigamist will ask the
final two contestants, Agnes and Bertha, to marry him. The executives have determined that
there is a 40% chance that Agnes will say yes and a 50% chance that Bertha will say yes.
(a) If Agnes and Bertha act independently, what is the probability that at least one of the
women will say yes?
(b) What is the probability of neither of the women saying yes?
5. You draw 2 cards from a well-shuffled deck of 52 cards. Find the probability that both cards
are Aces if the first card drawn is (a) replaced (b) not replaced.
Solutions: 1. 1/4 2. 1/36 3. 2/6 4. (a) 0.70 (b) 0.30 5. (a) 4/52×4/52 (b) 4/52×3/51
Lab Exercises Textbook Reading 4.1, 4.2 (skip Baye’s Theorem)
1. The manager of a Marvin Gardens, a large apartment complex, provides the following
probabilities to estimate the number of vacancies that will exist next month:
Vacancies Probability
0 0.05
1 0.15
2 0.35
3 0.25
4 0.10
5 0.10
A: Are these valid probability assignments?
B: Find the probability there are (a) no vacancies? (b) at least 4 vacancies? (c) at most 2?
2. If the probabilities are 0.05, 0.14, 0.17, 0.33, 0.20 and 0.11 that consumers will rate a new
product: very poor, poor, fair, good, very good, or excellent, respectively, what are the
probabilities that a consumer selected at random will rate the new product:
(a) very poor or poor? (b) good, very good, or excellent?
(c) good, if you know that the rating is in the group (good, very good or excellent) above?
Business Statistics
Lecture 4: Basic Probability Concepts
1. Determine the following probabilities:
(a) Drawing either an Ace or a Spade from a well-shuffled deck of 52 cards?
(b) Drawing either a Red Ace or a Spade? (c) Drawing neither an Ace nor a Spade?
Solutions: 1. (a) 16/52 (b) 15/52 (c) 36/52
Multiplication Law and Independent Events
1. You flip a coin twice. What is the probability of obtaining heads on both flips?
2. You roll a pair of six-sided dice. Find the probability that both die rolled come up 5’s.
3. You roll one six-sided die. Find the probability of rolling either a 2 or a 5.
4. From its TV studio’s in Bountiful, Reality TV is marketing a new reality TV series called
“Who Wants To Marry a Bigamist”. In the exciting final episode the bigamist will ask the
final two contestants, Agnes and Bertha, to marry him. The executives have determined that
there is a 40% chance that Agnes will say yes and a 50% chance that Bertha will say yes.
(a) If Agnes and Bertha act independently, what is the probability that at least one of the
women will say yes?
(b) What is the probability of neither of the women saying yes?
5. You draw 2 cards from a well-shuffled deck of 52 cards. Find the probability that both cards
are Aces if the first card drawn is (a) replaced (b) not replaced.
Solutions: 1. 1/4 2. 1/36 3. 2/6 4. (a) 0.70 (b) 0.30 5. (a) 4/52×4/52 (b) 4/52×3/51
Lab Exercises Textbook Reading 4.1, 4.2 (skip Baye’s Theorem)
1. The manager of a Marvin Gardens, a large apartment complex, provides the following
probabilities to estimate the number of vacancies that will exist next month:
Vacancies Probability
0 0.05
1 0.15
2 0.35
3 0.25
4 0.10
5 0.10
A: Are these valid probability assignments?
B: Find the probability there are (a) no vacancies? (b) at least 4 vacancies? (c) at most 2?
2. If the probabilities are 0.05, 0.14, 0.17, 0.33, 0.20 and 0.11 that consumers will rate a new
product: very poor, poor, fair, good, very good, or excellent, respectively, what are the
probabilities that a consumer selected at random will rate the new product:
(a) very poor or poor? (b) good, very good, or excellent?
(c) good, if you know that the rating is in the group (good, very good or excellent) above?
