Question

In this activity, you will predict the probability of an event from the relative frequency of the event. Pablo has some one-, five-, ten-, and twenty-dollar bills in his wallet. He randomly pulls one bill out of his wallet and replaces it. He does this 40 times as part of an experiment. The table shows the number of times Pablo pulls out each bill.

Bill Value Number of Times Picked
$1 6
$5 16
$10 10
$20 8

Part A
What is the relative frequency of drawing a one-dollar bill?

Part B
What is the relative frequency of drawing a five-dollar bill?

Part C
What is the relative frequency of drawing a ten-dollar bill?

Part D
What is the relative frequency of drawing a twenty-dollar bill?

Part E
Which type of bill is Pablo most likely to have the most of? How do you know?

Part F
Which type of bill is Pablo most likely to have the least of? How do you know?

Part G
Would you be surprised if Pablo had fewer twenty-dollar bills than one-dollar bills? What if he had fewer tens than ones? Why or why not?

Answer 1

Part A

6/40 = 0.15

Part B

16/40 = 0.4

Part C

10/40 = 0.25

Part D

8/40 = 0.20

Part E

The relative frequency of drawing a five-dollar bill is higher than the other relative frequencies. So, I can predict that Pablo is most likely to have more five-dollar bills than any of the others.

Part F

The relative frequency of drawing a one-dollar bill is lower than the other relative frequencies. So, I can predict that Pablo is most likely to have fewer one-dollar bills than bills of any other denomination.

Part G

It would not be a surprise if Pablo had fewer twenties than ones. The experiment was conducted only 40 times, and the numbers of times one-, ten-, and twenty-dollar bills were drawn are not very far apart. So, the number of twenties could be more or less than the number of ones. The same goes for tens and ones.

If you're on Plato an on slide 20 this Answer is for you:

If Pablo does an experiment 100 times, will the relative frequency be more accurate or less accurate than if he did the experiment 40 times? Why?

Answer: As the number of trials increases, the relative frequency becomes closer to the probability of the event. So, the relative frequency would be more accurate if the experiment were repeated 100 times rather than 40 times.