Probability in the Business Setting Answers

Jeremy randomly selected a round tile and a square tile from the sets shown below. What is the probability that Jeremy selected either two blue tiles or two white tiles?

You are playing a game in which you randomly select one square tile and one round tile from the sets shown below. Before you select your tiles, you try to guess which combination you will pick. Of the four possible guesses listed below, which one will give you the greatest chance of success?

Sharon is considering trying to open a new business within the next few years, and she is doing research to determine what kind of businesses tend to be successful. So far, she has compiled two tables. 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. 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 retail establishment to succeed and earn profits of $50,000 or more, or whether it is more likely for a new service establishment to succeed and earn profits of $25,000 or less, 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%).

A high school guidance counselor wants to find the probability that students who study geometry as freshmen will go on to study calculus before graduating. To do this, he has constructed a table, shown below, which shows the number of students who study geometry as freshmen in a given year, and the number of those students who study calculus before graduating.Year200020012002200320042005Geometry Students680577822743859804Calculus Students391336512374465361Which year had the highest experimental probability that a freshman studying geometry would take a calculus class before graduation?

Barry put all of the tiles shown below into a bag, then randomly pulled out one round one and one square one. What is the probability that Barry drew two red tiles?

Gareth selected a tile randomly from the set shown below. What is the probability that he selected a yellow tile or a tile with an odd number?

You have a spinner, shown below. You wish to test its fairness, so you conduct several trials in which you repeatedly spin the spinner and record how many times you come up with a result of violet. Your results are shown in the table next to the spinner. Trial 1 2 3 4 Times Spun 85 156 34 127 Times Violet 10 18 2 14 Calculate the experimental probability of your spinner showing a result of violet, written as a percentage to two decimal places.

What is the probability of rolling a prime number of a standard 20-sided die? (1 is not a prime number.)

Jeremy randomly selected a round tile and a square tile from the sets shown below. What is the probability that Jeremy selected either two blue tiles or two white tiles?

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 60 157 49 105 81 # of Blues 13 19 7 10 11 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%).

A city keeps track of the number of new small businesses which open in any given year, as well as how many of those new businesses report profit in excess of their initial investment after one year’s time. An example of the data collected can be viewed in the table below.Year19981999200020012002New781699626730762Profitable311205217264244If 684 new small businesses opened in 2003, approximately how many of them could be expected to turn a profit in excess of their initial investment by 2004?

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