1. Five coins are tossed.
a. Give an example of a simple event.
Which of the following is a simple event
Getting a head on no coins
Getting a head on the fifth coin and a tail on the third coin
Getting a tail on all coins
Getting a tail on the second coin
b. Give an example of a joint event.
Which of the following is a joint event
Not getting a head on the first coin
Getting a head or a tail on the second coin
Getting a head on the second coin and a head on the fourth coin
Not getting a tail on the second coin
c. What is the complement of getting a tail on the third coin
d. What does the sample space consist of
2. Use the contingency table to the right to determine the probability of events.
| Table Data |
B |
B' |
| A |
60 |
60 |
| A' |
80 |
90 |
a. What is the probability of event A?
b. What is the probability of event A'?
c. What is the probability of event A and B?
d. What is the probability of event A or B?
3. For each of the following, indicate whether the type of probability involved is an example of a priori probability, empirical probability, or subjective probability.
a. Upper A certain model will win the beauty contestA certain model will win the beauty contest.
b. The next roll of a fair die will land on the sixThe next roll of a fair die will land on the six.
c. According to census-based projections, a city's population will increase by 1.2% next year.
d. Upper A certain actor will win the award A certain actor will win the award.
4. For the following, state whether the events created are mutually exclusive and collectively exhaustive.
A product was classified as defective or not defective.
Choose the correct answer below.
A. The events are both mutually exclusive and collectively exhaustive.
B.The events are only mutually exclusive.
C. The events are only collectively exhaustive.
D. The events are neither mutually exclusive nor collectively exhaustive.
5. Which of the following events occur with a probability of zero
a. An airplane that is both in the air and on the groundAn airplane that is both in the air and on the ground
b. An individual who runs quickly and swims slowly An individual who runs quickly and swims slowly
c. An organism that is neither an animal nor a plant An organism that is neither an animal nor a plant
d. Upper A product that is neither foreign nor domestic
6. Do males or females feel more tense or stressed out at work? A survey of employed adults conducted online by a company on behalf of a research organization revealed the data in the contingency table shown to the right. Complete parts (a) through (d) below.
| Gender |
Tense/Stressed at Work |
Not Tense/Stressed at Work |
Total |
| Male |
110 |
370 |
480 |
| Female |
315 |
280 |
595 |
| Total |
425 |
650 |
1075 |
a. What is the probability that a randomly selected person's gender is female?
b. What is the probability that a randomly selected person feels tense or stressed out at work and is female?
c. What is the probability that a randomly selected person feels tense or stressed out at work or is female?
d. Explain the difference in the results in (b) and (c).
7. A survey about social media reported that 78% of B2B marketers (marketers that focus primarily on attracting businesses) plan to increase their use of social media, as compared to 56% of B2C marketers (marketers that primarily target consumers). The survey was based on 1,403 B2B marketers and 1,633 B2C marketers. The accompanying table summarizes the results. Complete parts (a) through (d) below.
| Increase Social Media Use |
B2B Marketer |
B2C Marketer |
Total |
| Yes |
1100 |
922 |
2022 |
| No |
303 |
711 |
1014 |
| Total |
1403 |
1633 |
3036 |
a. What is the probability that a randomly selected respondent plans to increase use of social media
b. What is the probability that a randomly selected respondent is a B2C marketer?
c. What is the probability that a randomly selected respondent plans to increase use of social media or is a B2C marketer?
d. Explain the difference in the results in (b) and (c).
8. Use the contingency table below to find the following probabilities.
| Table Data |
B |
B' |
| A |
30 |
10 |
| A' |
10 |
20 |
a. A|B
b. A|B'
c. A'|B'
d. Are events A and B independent?
9. If P(A)=0.80.8, P(B)=0.60.6, and A and B are independent, find P(A and B).
10. If P(A)=0.4, P(B)=0.9, and P(A and B)= 0.32, are A and B independent?
A.Yes
B. No
C. Not enough information
11.
A standard deck of cards is being used to play a game. There are four suits (hearts, diamonds, clubs, and spades), each having 13 faces (ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen, and king), making a total of 52 cards. This complete deck is thoroughly mixed, and you will receive the first 2 cards from the deck without replacement. Complete parts (a) through (d).
a. What is the probability that both cards are heartshearts?
b. What is the probability that the first card is a 9 and the second card is a 5 or a 6?
c. If you were sampling with replacement, what would be the answer in (a)?
d. In the game of? blackjack, the picture cards? (jack, queen, king) count as 10 points, and the ace counts as either 1 or 11 points. All other cards are counted at their face value. Blackjack is achieved if 2 cards total 21 points. What is the probability of getting blackjack in this problem?
12. If there are nine multiple-choice questions on an exam, each having four possible answers, how many different sequences of answers are there?
13. A lock on a bank vault consists of three dials, each with 25 positions. In order for the vault to open, each of the three dials must be in the correct position.
a. How many different possible dial combinations are there for this lock?
b. What is the probability that if you randomly select a position on each dial, you will be able to open the bank vault?
c. Explain why? "dial combinations" are not mathematical combinations expressed by the equation nCx = n!/(x!(n-x)!)
14.
a. If a coin is tossed three times, how many different outcomes are possible?
b. If a six-sided die is tossed three times, how many different outcomes are possible?
c. Discuss the differences in your answers to (a) and (b).
15. A particular brand of women's jeans is available in five different sizes, three different colors, and two different styles. How many different jeans does the store manager need to order to have one pair of each type?
16. You would like to "build-your-own-burger" at a fast-food restaurant. There are seven different breads, five different cheeses, two different cold toppings, and two different sauces on the menu. If you want to include one choice from each of these ingredient categories, how many different burgers can you build?
17. There are nineteen teams in a high school baseball league. How many different orders of finish are possible for the first four positions?
18. How many different ways can a senior project manager and an associate project manager and a technician be selected for an analytics project if there are eleven data scientists available?
19. Fourteen members of a group of seventeen are to be selected to a team. How many ways are there to select these fourteen members?
20. A daily lottery is conducted in which 2 winning numbers are selected out of 39 numbers? (without duplication). How many different combinations of winning numbers are possible?