10.1
An experiment is performed where a 6-sided die is rolled and then a 3-color spinner is spun. The possible outcomes for each event are 1, 2, 3, 4, 5, and 6 for the 6-sided die and red (R), blue (B), and yellow (Y) for the 3-color spinner. Identify the sample space for this experiment.
{1R,2R,3R,4R,5R,6R,1B,2B,3B,4B,5B,6B,1Y,2Y,3Y,4Y,5Y,6Y}
Customer account "numbers" for a certain company consists of 2 letters followed by 5 single-digit numbers. How many different account numbers are possible if repetitions of letters and digits are allowed?
67,600,000
Liam and James are going to play video games this afternoon. Together, they have 41 video games. If they decide to randomly choose two video games, what is the probability that the two they choose will consist of each of their favorite video games? Assume they have different favorites. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
1/820 OR 0.001220
A student organization has 25 members. Assume that 18 students own a cat, 19 students own a dog, 11 students own a fish, and 13 students own both a cat and a dog. What is the probability that a randomly selected student will own either a cat or a dog? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
24/25 OR 0.96
Suppose that you and a friend are playing cards and decide to make a bet. If your friend draws two black cards in succession from a standard deck of 52 cards replacing the first card, you give him $30. Otherwise, he pays you $20. If the same bet was made 20 times, how much would you expect to win or lose? Round your answer to the nearest cent, if necessary.
WIN $150
Jesse has 217 songs on a playlist. He's categorized them in the following manner: 37 country, 20 folk, 24 jazz, 11 gospel, 43 pop, 28 rap, and 54 rock. If Jesse begins listening to his playlist on shuffle, what is the probability that the first song played is a jazz song?
24/217 OR 0.110599
You are ordering a new home theater system that consists of a TV, surround sound system, and DVD player. You can choose from 7 different TVs, 8 types of surround sound systems, and 23 types of DVD players. How many different home theater systems can you build?
1288
It is presentation day in class and your instructor is drawing names from a hat to determine the order of the presentations. If there are 19 students in the class, what is the probability that the first presentations will be by Mila, Todd, and Kelly, in that order? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
1/5814 OR 0.0000172
Suppose that the probability of randomly selecting a cookie with chocolate chips out of a variety tin is 0.45 and the probability of selecting a cookie with raisins is 0.32. If the probability of selecting a cookie with raisins and chocolate chips is 0.17, what is the probability that the cookie chosen has neither raisins nor chocolate chips? Round your answer to the nearest millionth, if necessary.
2/5 OR 0.4
Calculate the expected value of the scenario.
xi P(xi)
-$1.25 0.6
-$0.25 0.2
$0 0.1
$0.50 0.1
-$0.75
Suppose you receive a bouquet of flowers that contains 18 red roses, 7 white daisies, 10 yellow roses, and 15 red tulips. If you select a flower from the bouquet at random, what is the probability of getting a flower that is not red?
17/50 OR 0.34
There are 32 students in a high school senior class. In how many ways could the yearbook choose one student to win each category of Most Athletic, Class Clown, and Best School Spirit? Assume no student can win more than one category.
29,760
Kiara sets up a passcode on her tablet, which allows only eight-digit codes. A spy sneaks a look at Kiara's tablet and sees her fingerprints on the screen over eight numbers. What is the probability the spy is able to unlock the tablet on his first try? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
1/40320 OR 0.000025
Identify which situation involves mutually exclusive events.
A) Let Event consist of selecting a prime number and Event consist of selecting a positive number.
B) Let Event consist of selecting a yellow marble and Event consist of selecting an oval marble.
C) Let Event consist of selecting a person with blood type B and Event consist of selecting a person with blood type AB.
D) Let Event consist of selecting a red card and Event consist of selecting a King.
C
Jim likes to day-trade on the Internet. On a good day, he averages a $1100 gain. On a bad day, he averages a $700 loss. Suppose that he has good days 30% of the time, bad days 50% of the time, and the rest of the time he breaks even. What is the expected value for one day of Jim’s day-trading hobby?
-$20
The blood types of people are collected at a doctor’s office. The table shows the breakdown of patients per blood type. If a person from this group is selected at random, what is the probability that this person has type O blood?
BLOOD TYPE PATIENTS
A 65
B 55
O 65
AB 15
13/40 OR 0.325
The president of the college asked a fraternity to submit a list of 7 students to serve as security at a school function. They have 20 students who are available to help. In how many ways can the students be chosen?
77,520
Suppose the probability of school being canceled for snow is 0.25. What are the odds of school being canceled? Express your answer in the form a:b.
1:3
The following table shows the breakdown of opinions for both faculty and students in a recent survey about the new restructuring of the campus to include an Honors College. Find the probability that a randomly selected person is either neutral or in favor of the restructuring. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
CATEGROY FAVOR OPPOSE NEUTRAL TOTAL
FACULTY 16 16 13 45
STUDENTS 41 44 67 152
TOTAL 57 60 80 197
137/197 OR 0.685431
A shoe company conducts a survey to determine the expected value of online sales for their new line of shoes coming out next fall. Based on past years, they have observed the following data on the probability of selling different types of shoes in the new line. The company expects that 7966 people will visit the website for their new line on launch day. Note that some of the online shoppers will not make a purchase.
SHOE PRICE PROBABILITY
SNEAKER $72.99 4/25
HIGH HEEL $95.25 1/5
SANDALS $54.50 1/10
LOAFERS $38.75 2/25
How much should the company expect its shoppers to spend on the website on launch day? Round your answer to the nearest cent, if necessary.
$312,891.73
What is the probability that a randomly selected student from this poll would be a male who has decided not to vote in the upcoming election?
WILL YOU VOTE
MALE FEMALE
YES 17 22
NO 20 24
NOT DECIDED 21 26
2/13 OR 0.153846
A university is putting together a hiring committee of 6 members for the next university provost. The eligible pool of members consists of 10 administrative personnel, 5 faculty, and 9 students. In how many ways can the committee be formed if there must be 2 members chosen from each of the three subgroups?
16,200
There are 4 sets of balls numbered 1 through 6 placed in a bowl. If 4 balls are randomly chosen without replacement, find the probability that the balls have the same number. Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
1/1771
A company that makes dog treats is investigating whether a dog’s size affects if the dog enjoys the treat or not. The company asked 129 dog owners if their dog enjoyed the chicken-flavored chew sticks. If one response is selected at random, what is the probability the response indicated that the dog is small-sized given that they enjoyed the treat? Express your answer as a fraction in lowest terms or a decimal rounded to the nearest millionth.
SIZE ENJOYED DID NOT ENJOY
SMALL 3 21
MEDIUM 37 20
LARGE 43 5
3/83 OR 0.036145
In American roulette, the wheel contains the numbers 1 through 36, alternating between black and red. There are two green spaces numbered 0 and 00. A player places a bet of $0.25 on red to play the game. If the ball lands on red, the player gets a $0.25 for winning and receives the money back. If the ball does not land on red, then the player simply loses the $0.25 placed on the bet. Calculate the expected winnings on one game. Round your answer to the nearest cent.
-$0.01