10 Probability Problems in EXCEL

1. Lauren drinks a variety of soft drinks. Over the past month, she has had 17 diet colas, 3 cans of lemonade, and 5 cans of root beer in no particular order or pattern.
a. Given this history, what is the probability that her next drink will be a diet cola? Lemonade? Root beer?
b. What definition of probability did you use to answer this question?

2. A home improvement company in Cincinnati ran a promotion: If a customer bought new windows before December 10, then if Cincinnati had a white Christmas, the purchase would be free. In the fine print, a "white Christmas" was defined as four inches of snowfall on December 25. The National Weather Service summarized Christmas Day snowfall from 1893 to 2014 as follows:

Inches of snow Frequency
0 68
Trace 28
0.1- 0.4 11
0.5 - 0.9 7
1.0 - 2.9 6
3.0 or more 1

What is the probability that the company would have to reimburse customers who took this offer?

3. Consider the experiment of drawing two cards without replacement from a deck consisting of only the ace through 10 of a single suit (for example, only hearts).
a. Describe the outcomes of this experiment. List the elements of the sample space.
b. Define the event Ai to be the set of outcomes for which the sum of the values of the cards is i (with an ace =1). List the outcomes associated with Aifor i =3 to 19.
c. What is the probability of obtaining a sum of the two cards equaling from 3 to 19?

4. Three coins are dropped on a table.
a. List all possible outcomes in the sample space.
b. Find the probability associated with each outcome.

5. A market research company surveyed consumers to determine their ranked preferences of energy drinks among the brands Monster, Red Bull, and Rockstar.
a. What are the outcomes of this experiment for one respondent?
b. What is the probability that one respondent will rank Red Bull first?
c. What is the probability that two respondents will both rank Red Bull first?

6. Refer to the card scenario described in Problem 3.a. Let A be the event "total card value is odd." Find P(A) and P(Ac).
b. What is the probability that the sum of the two cards will be more than 14?
c. What is the probably that the sum of the two cards will not exceed 12?

7. Refer to the coin scenario described in Problem 4.
a. Let A be the event "exactly two heads." Find P(A).
b. Let B be the event "at most one head." Find P(B).
c. Let C be the event "at least two heads." Find P(C).
d. Are the events A and B mutually exclusive? Find P(A or B).
e. Are the events A and C mutually exclusive? Find P(A or C).

8. Roulette is played at a table similar to the one in Figure 5.290. A wheel with the numbers 1 through 36 (evenly distributed with the colors red and black) and two green numbers, 0 and 00, rotate in a shallow bowl with a curved wall. A small ball is spun on the inside of the wall and drops into a pocket corresponding to one of the numbers. Players may make 11 different types of bets by placing chips on different areas of the table. These include bets on a single number, two adjacent numbers, a row of three numbers, a block of four numbers, two adjacent rows of six numbers, and the five number combinations of 0, 00, 1, 2, and 3; bets on the numbers 1-18 or 19-36; the first, second, or third group of 12 numbers; a column of 12 numbers; even or odd; and red or black. Payoffs differ by bet. For instance, a single-number bet pays 35 to 1 if it vins; a three-number bet pays 11 to 1; a column bet pays 2 to 1; and a color bet pays even money. Define the following events: C1 = column 1 number, C2 = column 2 number, C3 = column 3 number, O = odd number, E = even number, G = green number, F12 = first 12 numbers, S12 = second 12 numbers, and T12 = third 12 numbers. a. Find the probability of each of these events. b. Find PG or O), PO or F12), P(C1 or C3), P(E and F12), P(E or F12), P(S12 and T12), and PCO or C2).

9. Students in the new MBA class at a state university have the following specialization profile:
Finance 83
Marketing 36
Operations and Supply Chain Management 72
Information Systems 59
Find the probability that a student is either a finance or a marketing major.
Are the events finance specialization and marketing specialization mutually exclusive? If so, what assumption must be made?

10. An airline tracks data on its flight arrivals. Over the past six months, 70 flights on one route arrived early, 150 arrived on time, 15 were late, and 25 were canceled.
a. What is the probability that a flight is early? On time? Late? Canceled?
b. Are these outcomes mutually exclusive?
c. What is the probability that a flight is either early or on time?