Probability Notation
What does the notation P(A∩B) signify?
The probability that both events A and B occur simultaneously.
If you were to flip a coin 40 times, how many times would you expect to get Tails
40*.5=20
In a probability diagram, what does the sum of the probabilities on each branch equal?
1
Define complementary events.
Answers may vary
Choosing between turkey and not turkey; if you have turkey, you don't have the option of not having turkey.
Explain what P(A∪B) represents.
The probability that either event A or event B occurs (or both).
How would you denote the probability of not finding a turkey in your Thanksgiving feast?
P(Turkey’) or P(Turkey^c)
A family plans to serve 3 types of pie, and each guest has an independent 1/3 chance of choosing any pie. If there are 12 guests, what is the expected number of each type of pie chosen?
For each type of pie, E=12⋅1/3=4 guests expected to choose each type of pie.
Create a probability tree diagram for a Thanksgiving dinner where each guest can choose between turkey or ham and then can choose between two sides, mashed potatoes or green beans.
The tree will have 4 outcomes: (Turkey, Mashed Potatoes), (Turkey, Green Beans), (Ham, Mashed Potatoes), (Ham, Green Beans).
If the probability of having cranberry sauce at dinner is 0.3, what is the probability that you will not have cranberry sauce?
P(Not Cranberry Sauce)=1-0.3=0.7
Define mutually exclusive events using a Thanksgiving theme.
Answers may vary
Example: Events like having eggnog vs. having cranberry juice cannot happen at the same time in your glass, so they are mutually exclusive.
If the chance of getting a slice of pie is 0.4, what is the probability of not getting pie at the feast?
What is .6?
P(Not Pie)=1-0.4=0.6
Explain why the expected number of guests at a Thanksgiving dinner may not equal the actual number present.
The expected number is an average based on RSVPs and may differ from the actual turnout.
How can a probability tree diagram help you decide how many side dishes to prepare for Thanksgiving?
It helps visualize and calculate the probabilities of guests choosing certain side dishes based on preferences.
What is the probability of an impossible event?
Explain the difference between discrete and continuous random variables.
Thanksgiving Themed Answer: Discrete variables might count the number of pies (whole numbers), while continuous variables could measure the amount of gravy (any value).
In a probability diagram for Thanksgiving desserts, what does the sum of the probabilities of choosing pumpkin pie, apple pie, and pecan pie equal?
The sum of the probabilities must equal 1 (100% of dessert choices).
Write an equation representing the expected number of people who will eat dessert if 80% of guests usually do?
E(n)=n⋅0.8
How can you use a Venn diagram to find the probability of either event A or event B occurring?
Calculate the total area covered by both circles and subtract the area of the intersection.
A family plans to have either pumpkin pie or apple pie for dessert. If the probability of choosing pumpkin pie is 0.65, what is the probability that the family will choose apple pie?
P(Apple Pie)=1−P(Pumpkin Pie) =1−0.65=0.35
Identify the 3 acceptable formats of representing probabilities.
Decimal, Percent, Fractions
A family is considering serving either pumpkin pie or pecan pie for dessert. If the probability of serving pumpkin pie is 0.7, what is the probability of serving pecan pie, and how would you explain or show the relationship between these events using complementary probabilities?
The probability of serving pecan pie is P(Pecan)=1-P(Pumpkin)=1-0.7=0.3. The events are complementary because one dessert being served means the other cannot be served at the same time.
A player has a 54% shooting percentage. What is the expected number of successful shots if they take 8 free throws, 3 3-pointers, and 2 regular 2-point shots?
About 7 successful shots
7.02=.54x(8+3+2)
Create a sample venn diagram of your Friendsgiving dessert options. Write or prepare a verbal description with the diagram.
Answers will very.
In a Thanksgiving feast, if you have a 60% chance of choosing turkey and a 40% chance of choosing ham, calculate the probability that at least one guest will choose turkey if there are 5 guests.
Use the complement: P(at least one turkey)=1-P(no turkey)=1-(0.4^5)=1-0.01024=0.98976
Identify whether the statement below is true. Justify.
"The probability of an event can only be between 0 and 1."
True, because an outcome is a portion of a larger sample space representing the whole, or 1 (equal to 100%).