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# Probability Problem Set: Venn Diagrams, Probability of Selecting, Probability of Failure

1. The Venn diagram displays the results of all of the register voters in the county. What is the probability that a registered voter in the county vote in the election?

2. A certain virus infected one in every 200 people. A test used to detect the virus in a person is positive 99% of the time if the person has the virus and 1% of the time if the person does not have the virus. (this 1% is called a false positive). Let A be the event "the person is infected" and B is the event "the person tests positive. "Find the probability, given a person tests positive, that the person really is infected. If the person tests positive, what is the probability that the person is infected.

3) The following probability distribution describes the number of dogs per household in a small town.
a) What is the probability of randomly selecting a household that has fewer than two dogs?
b) What is the probability of randomly selecting a household that has at least four dogs?
c) What is the probability randomly selecting a household that has between one to three dogs?

4) Assume the probability that you will make a sale on any given telephone call is 0.74. Find the probability that you (a) make your first sale on the 5th call, (b) make your first sale on the first, second, third, or fourth call, and (c) you do not make a sale on one of the first 4 calls.

a) Find the probability that you make your first sale on the 5th call.
b) Find the probability that you make your first sale on the first, second, third or fourth call.
c) Find the probability you do not make a sale on any of the first four calls.

5) You are taking a multiple choices quiz that consists of 4 questions. Each question has 5 possible answers,
Only one of which is correct. To complete the quiz, you randomly guess the answers to each question.
Find the probability of guessing (a) exactly 3 answers correctly, (b) at least 3 answers correctly, or © less than

a) Find the probability of guessing exactly 3 answers correctly.
b) Find the probability of guessing a least 3 answers correctly.
c) Find the probability of guessing less than 3 answers correctly.

9) Consider a company that selects employees for random drug tests. The company uses a computer to select randomly employee's numbers that range from 1 to 7868. Find the probability of selecting a number less than 1500.00. Probability of selecting a number less than 1500.

10) In a state lottery, you must select 5 numbers (in any order) out of 40 correctly to win the top prize.

a) How many ways can 5 numbers are chosen from 40 numbers?
b) You purchase one lottery ticket. What is the probability of winning the top prize?

11) In a survey, 50% of students at a state university live in on-campus. Of these 50%, 4 out
Of 10 said that on-campus housing is too expensive.

a) Find the probability that a randomly selected student lives in on-campus housing and thinks that on campus housing is too expensive.
b) Given that a randomly selected student liven in on-campus housing, find the probability that he or she does not think that on-campus housing is too expensive.

13) In the following probability distribution, a sociologist surveyed the households in a small town. The random variable x represents the number of dependent children in the households. Determine the missing probability in this distribution

17) In an 8-team double elimination tournament, the winning team may play 4, 5, 6, or 7 games. Based on the results of a page of a large number of such tournaments, there is a probability of 0.1335 of winning in 4 games, 0.3355 of winning in 5, 0.3505 of winning in 6, and 0.1805 of winning in 7 games.

a) Find the mean number of games played by the winner of an 8 team double elimination.
b) Find the standard deviation of the probability distribution.
c) Which of the statement applies? Consider the mean and standard deviation/
a) It is unusual for a team to win in 6 games?
b) It is not unusual for a team to win in 4 games?
c) It is unusual for a team to win in 4 games?

18) In how many ways cab the numbers 6,7,8,9 and 0, be arranged without repetition for a five digit identification number?

20) A card is selected at random from a standard deviation deck. Find the probability?
P (randomly selecting a club or an 8) =
P (randomly selecting a red suit or a king) =
P (randomly selecting a 5 or a face card) =

15) The mean number of business failure per day in a certain region of the United States was about
6 failure/day. Find the probability that (a) exactly 10 business fail in any given day, (b) a least
10 business will fail in any one day, and © less than 10 business will fail in any one day.
Find the probability using the Poisson distribution.

a) Find the probability of exactly 10 failures on any given day.
b) Find the probability of a least 10 failure on any given day.
c) Find the probability of less than 10 failures on any given day.

21) The table shows the results of a survey in which 178 families were asked if they own a home and
If they will be purchasing a new vehicle this year.

Own a Home

a) Find the probability that a randomly selected family is buying a new car this year given that they own a home.
b) Find the probability that a randomly selected family is buying a new car this year and owns a home.

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