Probability Calculations
1. Compute the probability of 4 successes in a random sample of size n equals 15 obtained from a population of size N equals 60 that contains 29 successes. The probability of 4 successes is ___.
2. There are two letters X and Y. If repetitions such as XX are permitted, how many two-letter permutations are possible?
3. A corporation takes delivery of some new machinery that must be installed and checked before it becomes available to use. The corporation is sure that it will take no more than 10 days for this installation and check to take place. Let A be the event “it will be more than 5 days before the machinery becomes available” and B be the event “it will be less than 7 days before the machinery becomes available.” Complete parts a through g below.
a. Describe the event that is the complement of A.
b. Describe the event that is the intersection of events A and B.
c. Describe the event that is the union of events A and B.
d. Are events A and B mutually exclusive?
e. Are events A and B collectively exhaustive?
f. The event left parenthesis Upper A intersect Upper B right parenthesis union left parenthesis Upper A overbar intersect Upper B right parenthesis is equivalent to what event?
g. The event Upper A union left parenthesis Upper A overbar intersect Upper B right parenthesis is equivalent to what event?
4. A Tree-branch model is particularly useful when there’s only one event of interest. True or False.
5. In a recent article it was reported that 35.4% of all high school students smoke cigarettes. 65% of these students plan on going to college. What is the probability that a randomly selected student smokes cigarettes and plans on going to college?
6. The number of customers that are served at a fast food restaurant between noon and 2:00 p.m. is an example of a discrete random variable. True or False
7. One characteristic of the binomial distribution is that the outcome of one trial does not affect the outcome of any other trial. True or False
8. For a binomial probability function with P equals 0.5 and n equals 18, find the probability that the number of successes is equal to 9 and the probability that the number of successes is fewer than 7. P(9 successes) equals__ and P(fewer than 7successes) equals ___(Round to three decimal places as needed
9. A campus student club distributed material about membership to new students attending an orientation meeting. Of those receiving this material 40% were men and 60% were women. Subsequently, it was found that 7% of the men and 9% of the women who received this material joined the club. Complete parts a and b below.
a. Find the probability that a randomly chosen new student who receives the membership material will join the club. (Round to four decimal places as needed
b. Find the probability that a randomly chosen new student who joins the club after receiving the membership material is a woman. (Round to four decimal places as needed
10. A basketball player shoots 60 free throws a day and historically makes 75 percent of them. What is the probability that he will make at most 80 percent tomorrow?
11. Use the sample space S defined below.
S= (E1, E2, E3, E4, E5, E6, E7, E8, E9, E10)
Given A= (E4, E6, E7, E9) and B= (E4, E5, E6, E8),
a. What is the intersection of A and B?
b. What is the union of A and B?
c. Is the union of A and B collectively exhaustive?
12. On the average, 2.4 customers per minute arrive at any one of the checkout counters of a grocery store. A hypergeometric distribution can be used to find out the probability that there will be no customers arriving at a checkout counter. True of False
13. For the following, indicate if a discrete or a continuous random variable provides the best definition. The number of cars that arrive each day for repair in a two dash person repair shop Choose the correct answer. Continuous or Discrete
14. On average, you receive 2.6 pieces of junk mail a day. Assume that the number of pieces of junk mail you receive each day follows the Poisson distribution. What is the expected number of pieces of junk mail you receive daily? A manager has available a pool of 9 employees who could be assigned to a project-monitoring task. 3 of the employees are women and 6 are men. 2 of the men are brothers. The manager is to make the assignment at random so that each of the 9 employees is equally likely to be chosen. Let A be the event “chosen employee is a man” and B the event “chosen employee is one of the brothers.”
a. Find the probability of A.
b. Find the probability of B.
c. Find the probability of the intersection of A and B.
(Round to three decimal places as needed.)
15. A Venn diagram provides an intuitive understanding of the addition rule. True or False
16. In a city of 140,000people, there are 19,000 women. What is the probability that a randomly selected person from the city will be a woman? (Round to three decimal places as needed.)
17. Assume that the number of network errors experienced in a day on a local area network (LAN) is distributed as a Poisson random variable. The mean number of network errors experienced in a day is 2.4. What is the probability that in any given day less than three network errors will occur? (Round to four decimal places as needed.)
18. If A and B are independent events with P(A) = 0.60 and P (A | B) = 0.60, then P(B) is:
19. The probabilities that may be computed by summing the corresponding row or column of a two-way table are called:
20. The probability that an employee at a company uses illegal drugs is 0.08. The probability than an employee is male is 0.55. Assuming that these events are independent, what is the probability that a randomly chosen employee is a male drug user?
21. Events A and B are said to be mutually exclusive if their intersection is the empty set. True or False.
22. If P(A) = 0.20, P(B) = 0.40, and P(A∩ B) = 0.08, then A and B are said to be:
