Vocabulary
Examples of Vocab
permutation scenarios
Combination Scenarios
Addition rule scenarios
100
What is the equation for the Addition rule?
P (A or B) = P(A) + P(b) - P(A and B)
100
Name an example of something that is Mutually Exclusive.
Tossing a coin (heads or tails), turning left and turning right, even and odd numbers on a die.
100
The P.S Bistro enters and meatball-making contest at a local food festival. There are four other restaurants in the running: Little Italy, Sicilian Sauce House, Roma, and Pisa Pizza. How many ways could the restaurants (including yours) come in 1st, 2nd, 3rd, 4th, and 5th?
5 * 4 * 3 * 2 * 1 = 120
100
A pizza shop offers nine toppings. No topping is used more than once. What is the probability that the toppings on a three-topping pizza are pepperoni, onions, and mushrooms?
3C3/9C3 = 1/84 = 1.19%
100
In a parking lot there are 105 vehicles. There are 41 Ford vehicles and 27 pick-up trucks. There are 14 Ford pick-up trucks in the lot. Find the probability that a randomly chosen car is a Ford or a pick-up truck.
P(Ford)+P(truck) - P(Ford + truck)
41/105 + 27/105 - 14/105 = 54/105 (51.4 %)
200
What is a Permutation?
calculation of the number of ways a particular set can be arranged.
200
Come up with an example of a Permutation.
Choosing a specific flavor of ice cream to be scooped first and then a second flavor to be scooped second.
200
There are 8 teams in the SLC: Badger, Burlington, Central, Delavan-Darien, Elkhorn, Union Grove, Waterford, and Wilmot. In the upcoming baseball season how many different final standings are possible? (assume there are no ties)
8! = 40,320
200
The number of 4-letter Combinations which can be made from the letters of the word DRIVEN is
6C4=6!4!(6−4)!=
6!4!2!=
72024×2=
156C4=
6!4!(6−4)!=
6!4!2!=
720/24×2=
15
200
Are the Event's Mutually Exclusive?
Event A: Randomly select a senior from a class
Event B: Randomly select a student with blue eyes
NOT mutually exclusive, why?
300
What is a Combination?
An arrangement of objects where the order in which the objects are selected does NOT matter.
300
Come up with an example of a combination.
When you're ordering a pizza, it doesn't matter whether you order it with ham, mushrooms, and olives or olives, mushrooms, and ham. You're getting the same pizza!
300
Up until now, you have been directing the kitchen staff yourself. It's time to promote three of your 12 kitchen employees to positions of greater responsibility. How many ways could you select 3 of the 12 to be promoted to the positions of head chef, sous chef, and pastry chef?
12P3 = 12!/(12-3!) = 12!/9! = 1320
300
At a local language school, 40% of the students are learning Spanish, 20% of the students are learning German, and 8% of the students are learning both Spanish and German. What is the probability that a randomly selected student is learning Spanish or German?
P(Spanish or German)=P(Spanish)+P(German)−P(Spanish and German)
=0.4+0.2−0.08
=0.52
400
What does Mutually Exclusive mean?
Two or more events that CANNOT happen at the same time.
400
When can you use the Addition rule? come up with an example.
Find the probability that a card randomly drawn from a deck is a face card or a heart.
P(face) + P(heart) - P(face + heart)
12/52 + 13/52 - 3/52 = 22/52 (42.3%)
400
How many different arrangements of letters of the word MATHEMATICS are possible?
Number of letters = 11
M = 2
A = 2
T = 2
Number of different arrangements = 11!/(2! 2! 2!)
= (11 × 10 × 9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1)/(2 × 1 × 2 × 1 × 2 × 1)
= 4989600
400
There are 50 students enrolled in the second year of a business degree program. During this semester, the students have to take some elective courses. 18 students decide to take an elective in psychology, 27 students decide to take an elective in philosophy, and 10 students decide to take an elective in both psychology and philosophy. What is the probability that a student takes an elective in psychology or philosophy?
P(psychology or philosophy)=P(psychology)+P(philosophy)−P(psychology and philosophy)
=1850+2750−1050
=0.7