Back[NW] Selecting a Jury
The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of eight students and ten faculty.
a. What is the probability of selecting a jury of all students?
Manufacturing An assembly line produces 10,000 automobile parts. Twenty percent of the parts are defective. An inspector randomly selects 10 of the parts
a. Use the Multiplication Rule (discussed in Section 3.2) to find the probability that none of the selected parts are defective. (Note that the events are dependent.)
A school is holding a fair raffle and a teacher is interested in predicting how many winners will be from her class. Determine which probability distribution she should use given the following information.
(A) There are 386 tickets, one for each student. Tickets are placed back in the pool after being chosen and 5 tickets are drawn.
Drawing Cards Suppose that you draw 3 cards without replacement from a standard 52-card deck. What is the probability that all 3 cards are aces?
In Problems 7–16, determine which of the following probability experiments represents a binomial experiment. If the probability experiment is not a binomial experiment, state why.
A random sample of 30 cars in a used car lot is obtained, and their mileages recorded.
If we sample from a small finite population without replacement, the binomial distribution should not be used because the events are not independent. If sampling is done without replacement and the outcomes belong to one of two types, we can use the hypergeometric distribution. If a population has A objects of one type (such as lottery numbers you selected), while the remaining B objects are of the other type (such as lottery numbers you didn’t select), and if n objects are sampled without replacement (such as six drawn lottery numbers), then the probability of getting x objects of type A and objects of type B is
In New Jersey’s Pick 6 lottery game, a bettor selects six numbers from 1 to 49 (without repetition), and a winning six-number combination is later randomly selected. Find the probability of getting exactly four winning numbers with one ticket.
[NW] Selecting a Jury
The grade appeal process at a university requires that a jury be structured by selecting five individuals randomly from a pool of eight students and ten faculty.
c. What is the probability of selecting a jury of two students and three faculty?
Playing Music on Random Setting
Suppose that a Spotify playlist has 13 tracks. After listening to all the songs, you decide that you like 5 of them. With the random feature on the playlist, each of the 13 songs is played once in random order. Find the probability that among the first two songs played:
a. You like both of them. Would this be unusual?
In the Dark A box containing twelve 40-watt light bulbs and eighteen 60-watt light bulbs is stored in your basement. Unfortunately, the box is stored in the dark and you need two 60-watt bulbs. What is the probability of randomly selecting two 60-watt bulbs from the box?
Packaging Error
Because of a manufacturing error, three cans of regular soda were accidentally filled with diet soda and placed into a 12-pack. Suppose that two cans are randomly selected from the 12-pack.
c. Determine the probability that exactly one is diet and one is regular?
Packaging Error
Because of a manufacturing error, three cans of regular soda were accidentally filled with diet soda and placed into a 12-pack. Suppose that two cans are randomly selected from the 12-pack.
b. Determine the probability that both contain regular soda. Would this be unusual?
A school is holding a fair raffle and a teacher is interested in predicting how many winners will be from her class. Determine which probability distribution she should use given the following information.
(B) There are 386 tickets, one for each student. Tickets are removed from the pool after being chosen and 5 tickets are drawn.
Find the probability of drawing a hand of 5 cards from a standard deck that contains exactly 2 hearts.
Selecting a Committee
Suppose that there are 55 Democrats and 45 Republicans in the U.S. Senate. A committee of seven senators is to be formed by selecting members of the Senate randomly.
b. What is the probability that the committee is composed of all Republicans?
Playing Music on Random Setting
Suppose that a Spotify playlist has 13 tracks. After listening to all the songs, you decide that you like 5 of them. With the random feature on the playlist, each of the 13 songs is played once in random order. Find the probability that among the first two songs played:
c. You like exactly one of them.