Randomness, Probability, and Simulations
Probability Rules
Conditional Probability and Independence
Probability Vocabulary
Random Variables
Thanksgiving Trivia
100
This law says that in many repetitions of the same chance process, the proportion of times that a particular outcome occurs will approach its probability.
The law of large numbers
100
Is the following a valid probability model?
What is no (the sum is greater that 100%)
100
A coin is tossed 3 times. What is the probability that it lands on heads exactly one time?
What is...
0.375
100
Events that do not impact each other's probability.
What is...
independent
100
If a probability distribution is symmetric, which of the following statements must be true?
a. The distribution is normal.
b. The distribution is uniform.
c. The distribution is bimodal.
d. The mean of the distribution is equal to the median of the distribution.
e. The interquartile range of the distribution is equal to the standard deviation of the distribution.
The mean of the distribution is equal to the median of the distribution.
100
FACT OR FICTION: THANKSGIVING IS HELD ON THE FINAL THURSDAY OF NOVEMBER EACH YEAR.
Fiction. In 1863, President Abraham Lincoln designated the last Thursday in November as a national day of thanksgiving. However, in 1939, after a request from the National Retail Dry Goods Association, President Franklin Roosevelt decreed that the holiday should always be celebrated on the fourth Thursday of the month(and never the occasional fifth, as occurred in 1939) in order to extend the holiday shopping season by a week.
200
If I toss a fair coin 5 times and the outcomes are TTTTT, then the probability that tails appears on the next toss is...
What is 1/2?
200
Use the probability to find the probability that x > 27.
What is 0.32?
200
Two hundred people were surveyed about whether or not they like recreational reading and academic reading. The following two-way table displays data for the sample of people who responded to the survey. 
What percent of people liked recreational reading given that they liked academic reading?
What is 136/152 = 89.5%
200
two events that cannot occur simultaneously
What is....
mutually exclusive or disjoint
200
The quality control manager at a factory records the number of equipment breakdowns each day. Let the random variable Y represent the number of breakdowns in one day. The standard deviation of Y is 0.28. Give an interpretation of the standard deviation.
On average, the number of breakdowns per day varies from the mean by about 0.28.
200
FACT OR FICTION: ONE OF AMERICA’S FOUNDING FATHERS THOUGHT THE TURKEY SHOULD BE THE NATIONAL BIRD OF THE UNITED STATES.
Fact. In a letter to his daughter sent in 1784, Benjamin Franklin suggested that the wild turkey would be a more appropriate national symbol for the newly independent United States than the bald eagle
300
The probability that Shruti succeeds at any given free-throw is 80 percent. She was curious about how many free-throws she can expect to succeed in a sample of 12 free-throws.
She simulated 25 samples of 12 free-throws where each free-throw had a 0.80 probability of being a success.
Shruti counted how many free-throws were successes in each simulated sample. Here are her results:
Use her results to estimate the probability that she succeeds at 10 or more free-throws in a sample of 12 free-throws.
What is 20/25 = 80%?
300
Given two mutually exclusive events, A and B, what is the probability that event A or event B occurs?
What is ...
P(A or B)= P(A) + P(B)
300
Does this table show independence? Discuss.
What is no? Academic readers were more likely to like recreational reading than people who didn't like academic reading. (136/152 vs 40/48)
300
two events that cannot occur together, but one must happen
What is...
complementary
300
$220,700
300
3. FACT OR FICTION: IN 1863, ABRAHAM LINCOLN BECAME THE FIRST AMERICAN PRESIDENT TO PROCLAIM A NATIONAL DAY OF THANKSGIVING.
Fiction. George Washington, John Adams and James Madison all issued proclamations urging Americans to observe days of thanksgiving
400
Mr. Woyna has missed on his last 5 bets, but he claims that he's "due" to get the next one. Explain why he is an idiot.
Each game is independent and has no effect on the next game.
400
Employees at an office were surveyed about what types of hot beverages they drank that day. It was found that 50 percent of them drank coffee and 25 percent drank tea. The survey showed that 10 percent of the employees drank both coffee and tea.
For these employees, are the events "drank coffee" and "drank tea" mutually exclusive?
What is no, 10% drank both.
400
Abby, Bobby, Carlos, DeAnna, and Emily go to the bagel shop for lunch every Thursday. Each time, they randomly pick 2 of the group to pay for lunch by drawing names from a hat. Find the probability that Carlos and DeAnna end up paying for lunch.
What is (1/20)+ (1/20) = 1/10?
400
events that impact each other's probability
what is ...
dependent
400
1.25
400
FACT OR FICTION: MACY’S WAS THE FIRST AMERICAN DEPARTMENT STORE TO SPONSOR A PARADE IN CELEBRATION OF THANKSGIVING.
Fiction. The Philadelphia department store Gimbel’s had sponsored a parade in 1920, but the Macy’s parade, launched four years later, soon became a Thanksgiving tradition and the standard kickoff to the holiday shopping season.
500
A basketball player claims to make 47% of her shots from the field. We want to simulate the player taking sets of 10 shots, assuming that her claim is true. Describe how you would simulate a single shot.
Example:
Use 10 random two-digit numbers where 00 - 46 area a make and 47 - 99 are a miss.
500
Suppose C and D are two events such that P(C) = 0.6, P(D) = 0.45, and P(C or D) = 0.75. Find P(C and D).
What is 0.3?
500
90% of the people who have a particular disease will have a positive result on a given diagnostic test (90% accuracy). If 5% of a certain population has the disease, what percent of that population would test positive for the disease?
What is ...
14% or 0.14
500
contains all of the possible outcomes
what is...
sample space
500
A mathematics competition uses the following scoring procedure to discourage students from guessing (choosing an answer randomly) on the multiple-choice questions. For each correct response, the score is 7. For each question left unanswered, the score is 2. For each incorrect response, the score is 0. If there are 5 choices for each question, what is the minimum number of choices that the student must eliminate before it is advantageous to guess among the rest?
2
500
With 6 appearances, which cartoon character has appeared the most amount of times as a balloon in the Thanksgiving Day Parade?
Snoopy has appeared as a giant balloon in the Macy’s Thanksgiving Day Parade more times than any other character in history.