Randomness, Probability, and Simulation

A random outcome is one in which...

• There is a long term predictable pattern to the observed outcomes
• All outcomes are equally likely 
• Outcomes are haphazard or unpredictable in the long run
• We know which outcomes will occur ahead of time

Decide if the following outcome is random:
Flip a coin to decide who takes out the trash.
Is who takes out the trash random?

• Yes
• No

Decide if the following outcome is random:
Names are selected out of a hat to decide roommates for a dormitory. Is your roommate for the year random?

• Yes
• No

Decide if the following outcome is random:
A friend asks you to quickly name a professional sports team.  Is the sports team named random?

• Yes
• No

Suppose we want to select two students at random for a committee from a high school class containing 25 students.  If we evaluate the following random numbers two at a time from left to right, which two "students" would be selected?
Suppose we code each student with a unique number from 01-25:
470324127901249348872357335207

• 47 & 23 
• 03 & 24
• 24 & 12
• 4 & 7

Suppose 30% of cereal boxes contain a picture of LeBron James, 20% a picture of Steph Curry, and 50% a picture of Ben Simmons.  Which of the following digit assignments correctly models this situation?

• Let 1 = LeBron James; Let 2 = Steph Curry; Let 3 = Ben Simmons
• Let 0-3 = LeBron James; Let 4-5 = Steph Curry; Let 6-9 = Ben Simmons
• Let 1-3 = LeBron James; Let 4-5 = Steph Curry; Let 6-9 = Ben Simmons
• Let 0-2 = LeBron James; Let 3-4 = Steph Curry; Let 5-9 = Ben Simmons

Which is the best way to simulate choosing one student out of 12 to be the class president?

• roll a die and flip a coin
• roll a die
• spin a spinner with 4 sections
• flip a coin

The questions on a multiple choice test each have 6 answer choices. Which model can be used to simulate randomly selecting the correct answer on a 20 question multiple choice test?

• rolling a six-sided number cube 6 times
• rolling a six-sided number cube 20 times
• spinning a spinner with 4 equal sized sections 4 times
• choosing 1 marble in a bag of 20 different colored marbles

A certain brand of TV has a 50% chance of being defective. Which model could be used to determine the probability that when two TVs are chosen, they will both be defective?

• spin a spinner with 4 equal sections
• roll a die twice
• flip a coin twice
• flip a coin, then roll a die

Layla has 2 pairs of shoes and 6 pairs of socks. If each pair of socks and each pair of shoes is equally like to be chosen, which is the best simulation to show the probability of choosing any given combination?

• roll a die and flip a coin
• roll a die two times
• flip a coin 6 times
• flip a coin 2 times