# Chapter 1. Probability 2 (the roulette wheel)

## Introduction

Statistical Applets Select an event (set of outcomes) of interest and a number of spins on the wheel. The outcome of each spin will be displayed as a bar graph of individual results and as a proportion of times the event of interest occurred. Check the box to show the true probability of the event. Click RESET at any time to start over.

Click the "Quiz Me" button to complete the activity.

The American roulette wheel has 38 numbered slots: 1 through 36, 0, and 00. If the wheel is fair, the ball will be equally likely to end up in any slot.

In this applet, you can study the behavior of the wheel through a small number of spins, as well as a large number. You can also investigate the probability of certain sets of outcomes (events); does the empirical evidence from the wheel agree with the theoretical model that says:

P(A) = (Number of Outcomes in A) / (Number of Possible Outcomes) ### Question 1.1

The applet initially has “Spin a 2” as the event of choice. What is the probability of a 2 on the roulette wheel? Give your answer to 4 decimal places.
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2
Incorrect. Only one slot on the wheel has the number 2 out of 38 slots.
Correct. The probability of a 2 is 1/38 = 0.0263.

### Question 1.2

Spin the when 5 times. Do you expect to see a 2? 7zVRuryDpphPQjDfxtKbZg==

1
Incorrect. Something that should happen rarely (less than 5% of the time) would not be expected to occur in five attempts.
Correct. Something that should happen rarely (less than 5% of the time) would not be expected to occur in five attempts.

### Question 1.3

Reset the applet and change the sample size to 2000 spins. Do you expect to see a 2? esgbknumN3x7TOMm7lo9Vw==

1
Incorrect. Something that should happen rarely (less than 5% of the time) will be expected to occur in many attempts.
Correct. Something that should happen rarely (less than 5% of the time) will be expected to occur in many attempts.

### Question 1.4

Change to spin a red number and five attempts. What is the probability the wheel lands on a red number? Give your answer to four decimal places.
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2
Incorrect. Eighteen slots on the wheel out of 38 slots are red.
Correct. The probability of a red is 18/38 = 0.4737.

### Question 1.5

Did you get a red? esgbknumN3x7TOMm7lo9Vw==

1
Incorrect. If the line in the middle of the output moved anywhere off 0, you got a red.
Correct. It would be highly unusual to not get a red in five spins.

### Question 1.6

Reset the applet and spin the wheel 2000 times. This is almost a “very large” number of attempts. What do you see in the center part of the window?
RjPD0yIPeSIdJmSOTGeuarLH0Jta+t6eW/rhKtowtunBaXxIg3PMiZRUuXYYTVeqJuU3JHNPgC/fGUXZxCgLngqqcoBQjN37Yal0iqS6dErNKt/2qnQYRScs55l5ywN1V2t//TUJ52oYABwBcVUkopVZwdf5lAtPdqPCrBQj+CY4TAAJ2q1hy/bsjwzZzUfHftrFaaleoBD2U61ZzaWzSpXVPx+wgzAavn0IVHUgayY=

1
Incorrect. Probabilities are about what can happen in the long term. For any event of interest, as the number of trials becomes large, the relative frequency of the event (in this case, the proportion of reds) becomes close to the true probability of the event.
Correct. Probabilities are about what can happen in the long term. For any event of interest, as the number of trials becomes large, the relative frequency of the event (in this case, the proportion of reds) becomes close to the true probability of the event.