Probability in the Business Setting Answers

Harold randomly selected one square tile and one round tile from the sets shown below. What is the probability that Harold selected a pink square tile, and either a red or a blue round tile?

If a letter of the alphabet is chosen at random, what is the probability that it will be a vowel? (Y is not a vowel.)

The two tables below show the success rates of several groups of businesses in a certain city. The first shows the number of businesses of several types started in Sharon’s city over the course of two years, and the number of those businesses which did not succeed and were forced to shut down within two years of opening. The second deals with separate records of successful new businesses, showing how much profit those new businesses turned over two years. Businesses on the boundary lines fall in the lower category.TypeFoodRetailFinancialServiceOpened3,1932,2801,8985,045Closed1,9771,6261,4433,548 Up to $25k$25-50k$50-75k$75-100kOver $100kFood945623601258114Retail81354834718863Financial3162441958651Service979739432174124Using the tables as experimental data, determine which of the following situations have a probability of at least 15.00%.I. a food establishment succeeding and earning $50,000 or moreII. a service establishment succeeding and earning between $25,000 and $75,000III. a retail establishment succeeding and earning no more than $50,000

What is an advantage that experimental probability has over theoretical probability?

You are the manager of a retail store, and you have been tasked with finding the return rate on a certain brand of laptop computers. You have assembled the data on the number of computers sold and the number returned over the past six months in the table below.MonthOctNovDecJanFebMarSold1,6211,7521,8481,6341,7251,780Returned223415421560330304Using the table as experimental data, if your store has 379 laptops returned in April, how many laptops are likely to have been sold in April?

Harold randomly selected one square tile and one round tile from the sets shown below. What is the probability that Harold selected a pink square tile, and either a red or a blue round tile?

Perry is considering trying to open a new business within the next few years, and he is doing research to determine what kind of businesses tend to be successful. So far, he has compiled two tables. The first shows the number of businesses of several types started in Perry’s city over the course of two years, and the number of those businesses which did not succeed and were forced to shut down within two years of opening. The second deals with separate records of successful new businesses, showing how much profit those new businesses turned over two years. Businesses on the boundary lines fall in the lower category. Type Food Retail Financial Service Opened 3,193 2,280 1,898 5,045 Closed 1,977 1,626 1,443 3,548 Up to $25k $25-50k $50-75k $75-100k Over $100k Food 945 623 601 258 114 Retail 813 548 347 188 63 Financial 316 244 195 86 51 Service 979 739 432 174 124 Using the tables as experimental data, determine whether it is more likely for a new food establishment to succeed and earn up to $25,000, or whether it is more likely for a new financial establishment to succeed and earn profits in either the $25,000-50,000 range or the $50,000-75,000 range, and how much more likely the one situation is than the other. Express all probabilities as percentages to two decimal places, and express differences by number of percentage points (for example, 23% is 5 percentage points greater than 18%).

Terrence is playing a game in which he will randomly select one square tile and one round tile from the tile sets shown below. Before he does so, he tries to guess which tiles he will draw. Of the four possible guesses listed below, which will give Terrence the highest chance of success?

You are the manager of a retail store, and you have been tasked with finding the return rate on a certain brand of laptop computers. You have assembled the data on the number of computers sold and the number returned over the past six months in the table below.MonthOctNovDecJanFebMarSold1,6211,7521,8481,6341,7251,780Returned223415421560330304Using the table as experimental data, if your store has 379 laptops returned in April, how many laptops are likely to have been sold in April?

Carolyn selected a tile randomly from the set shown below. What is the probability that she selected a white tile or a tile with an even number?

A restaurant manager wanted to get a better understanding of the tips her employees earn, so she decided to record the number of patrons her restaurant receives over the course of a week, as well as how many of those patrons left tips of at least 15%. The data she collected is in the table below.DayMonTueWedThuFriSatSunPatrons126106103126153165137Tippers82879368918364Which day of the week has the lowest experimental probability of patrons tipping at least 15%?

Which of the following is a pair of events which are mutually exclusive?

In order to better decide how to market a new line of clothing, Mary is researching the demographics of the customers of a certain clothing store. She counted the number of customers who visited the store over the course of a month, and found out how many of the customers were high school students. Her collected data is in the table below.Week1234Customers2,8483,1413,8613,911Students2,0331,9372,0761,721Mary predicts that the store will see 4,238 customers next week. Approximately how many high school students should the store expect next week?

Which of the following is a pair of events which are dependent on one another?

Lawrence decided to test the balance of his favorite six-sided die. To do so, over the course of a month, he wrote down the total number of rolls he made with it at his weekly gaming night, and how many of those rolls showed a result of six. His data may be seen in the table below.Week1234Rolls Made39215541Results of Six531111Find the experimental probability of Lawrence’s favorite die rolling a six, expressed as a percentage to two decimal places.

The two tables below show the success rates of several groups of businesses in a certain city. The first shows the number of businesses of several types started in Sharon’s city over the course of two years, and the number of those businesses which did not succeed and were forced to shut down within two years of opening. The second deals with separate records of successful new businesses, showing how much profit those new businesses turned over two years. Businesses on the boundary lines fall in the lower category.TypeFoodRetailFinancialServiceOpened3,1932,2801,8985,045Closed1,9771,6261,4433,548 Up to $25k$25-50k$50-75k$75-100kOver $100kFood945623601258114Retail81354834718863Financial3162441958651Service979739432174124Using the tables as experimental data, determine which of the following situations have a probability of at least 15.00%.I. a food establishment succeeding and earning $50,000 or moreII. a service establishment succeeding and earning between $25,000 and $75,000III. a retail establishment succeeding and earning no more than $50,000

Lawrence decided to test the balance of his favorite six-sided die. To do so, over the course of a month, he wrote down the total number of rolls he made with it at his weekly gaming night, and how many of those rolls showed a result of six. His data may be seen in the table below.Week1234Rolls Made39215541Results of Six531111Find the experimental probability of Lawrence’s favorite die rolling a six, expressed as a percentage to two decimal places.

A batch of tiles, shown below, is placed into a bag. Ariana randomly draws one tile from the bag, records it, puts it back in the bag, and draws another tile. What is the probability that Ariana will draw a purple tile first and a red tile second?

A restaurant manager wanted to get a better understanding of the tips her employees earn, so she decided to record the number of patrons her restaurant receives over the course of a week, as well as how many of those patrons left tips of at least 15%. The data she collected is in the table below.DayMonTueWedThuFriSatSunPatrons126106103126153165137Tippers82879368918364Which day of the week has the lowest experimental probability of patrons tipping at least 15%?

Say that you put the set of tiles shown below into a bag and conduct a series of trials in which you draw one tile randomly from the bag, record the color, and replace it. The table below shows the number of times in each set of trials that you drew a blue tile. Trial 1 2 3 4 5 # of Draws 54 36 80 22 75 # of Blues 18 11 20 4 32 Between the theoretical probability that you will draw a blue tile and the experimental probability that you will draw a blue tile, which is greater, and how much greater is it? Express all probabilities as percentages to two decimal places, and express differences by number of percentage points (for example, 12% is 2 percentage points greater than 10%).