# Probability: work each problem and show all work

**Question description**

1. Let S = {1, 2, 3, 4, 5, 6}, E = {2, 4, 6}, F = {1, 3, 5}, an G = {3, 4} Are the event F and G complementary?

2. Let S = {1, 2, 3, 4, 5, 6}, E = {1, 3, 5}, F = {2, 4, 6}, an G = {2, 3} Are the event F and G mutually exclusive?

3. Let S = { x, y, and z} be a sample space of an experiment with the outcomes.

x, y, and z. List all the events of this experiment.

4. An experiment consists of selecting a card from a standard deck of playing cards and noting whether the card is black (B) or red (R). Describe an appropriate sample space for this experiment.

5.An experiment consists of selecting a card from a standard deck of playing cards and noting whether the card is black (B) or red (R). What are the events of this experiment?

6. An experiment consists of tossing a coin, rolling a die, and observing the outcomes. Describe the event “A head is tossed and an odd number is rolled.”

7. A sample of two transistors taken from a local electronics store was examined to determine whether the transistors were defective (d) or nondefective (n). What is an appropriate sample space for this experiment?

8. In a television game show, the winner is asked to select three prizes from five different prizes, A, B, C, D, and E. Describing a sample space of possible outcomes (order is not important) determine the number of points there are in the sample space corresponding to a selection that includes A.

9. As part of a quality-control procedure, an inspector at Bristol Farms randomly selects ten eggs from each consignment of eggs he receives and records the number of broken eggs. Describe the event F that at least nine eggs are broken.

10. Let S = {4, 5, 6} be a sample associated with an experiment.

How many subsets of S contain the number 5 and the number 6?

11. The following breakdown of a total of 18,686 transportation fatalities that occured in 2007 was obtained from records compiled by the U.S. Department of Transportation (DOT).

Mode of Transportation |
Car |
Train |
Bicycle |
Plane |

Number of Fatalities |
16,525 |
842 |
698 |
538 |

What is the probability that a victim randomly selected from this list of transportation fatalities for 2007 died in a train or a plane accident? Round answer to two decimal places.

12. In a survey of 900 likely voters, the following question was asked: Do you support using cameras to identify red-light runners? The results of the survey follow:

Answer |
Strongly support |
Somewhat support |
Somewhat oppose |
Strongly Oppose |
Don’t know |

Respondents |
410 |
212 |
95 |
164 |
19 |

What is the probability that a person in the survey selected at random favors using cameras to identify red-light runners?

13. According to Mediamark
Research, 88 million out of 179 million adults in the United States correct
their vision by using prescription eyeglasses, bifocals, or contact lenses.
(Some respondents use more than one type.) What is the probability that an adult
selected at random from the adult population uses corrective lenses? Round your
answer to the nearest thousand^{th}.

14. One light bulb is selected at random from a lot of 110 light bulbs, of which 2% are defective. What is the probability that the light bulb selected is defective?.

15. If a ball is selected at random from an urn containing two red balls, three white balls, and five blue balls, what is the probability that it will be a white ball?

16. What is the probability of arriving at a traffic light when it is red if the red signal is flashed for 30 sec, the yellow signal for 5 sec, and the green signal for 40 sec?

17. The grade distribution for a certain class is shown in the table.

Grade |
A |
B |
C |
D |
F |

Frequency of Occurrence |
6 |
6 |
18 |
8 |
2 |

What is the probability that a student selected at random from this class received a passing grade (D or better)?

18. In a sweepstakes sponsored by Gemini Paper Products, 100,000 entries have been received. If 2 grand prize, 10 first prizes, 35 second prizes, and 600 third prizes are to be awarded, what is the probability that a person who has submitted one entry will win a prize?

19. In a survey conducted in 2007 of 954 adults 18 years old and older, the following question was asked: How are American companies doing on protecting the environment compared with companies in other countries? The results are summarized below:

Answer |
Behind |
Equal |
Ahead |
Don’t know |

Respondents |
382 |
236 |
240 |
96 |

If an adult in the survey selected at random, what is the probability that he or she said that American companies are equal or ahead on protecting the environment compared with companies in other countries? Round your answer to two decimal places.

20. A study conducted by the Corrections Department of a certain state revealed that 163,767 people out of a total adult population of 1,799,738 were under correctional supervision (on probation, parole, or in jail). What is the probability that a person selected at random from the adult population in that state is under correctional supervision?

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