Name: ___________________________________________ Date: ________________ Per: ____
UNIT 5 – Mutually Exclusive Events
Grading Rubric: Each section is worth 5 class-participation points and homework is 8 points as
follows.
•
Class Participation points: Do Now, We Do, You Do, and Exit ticket sections are fully
completed in class with all work and notes.
•
Homework points (2 points per question):
o
8 points – all parts of the question are complete and correct with work.
o
6 points – all parts are attempted with work/one part has a minor error.
o
4 points – all parts are attempted with work/all questions have minor errors.
o
2 points – some parts are not answered or work is missing.
o
1 point – major errors in answers and work.
These problems are practice for the next Unit test. You are expected to know the material in this
packet.
This packet will become part of your folder of work. After it is graded, the packet must be kept in
your folder. If you need to correct any portion of this, you will do corrections on separate paper
and label it with the section title and problem number.
The due date for the entire packet will be the next time the class meets after we have completed all
sections.
DUE DATE: _________________________
GRADING
Section
Do Now
We Do
You Do
Exit
POINTS
GRADE
Teacher Comments:
Class Participation Points
Homework Points
Name: __________________________________________ Date: _____________ Per: ____
Mutually Exclusive Events
DO NOW:
1. Andrea researched the history of 4,000 college students to see whether they were in Honors classes in High School and/or College. The results are displayed in the table shown. A person is to be selected at random out of the 4,000 former college students. Honors in Honors in College Not in Honors in College High School Not in Honors in High School 145 315 47 3493 Part A: What is the probability that the selected person was in Honors in college, given that the person was in Honors in High School? Part B: What is the probability that the selected student was in Honors in High School, given that the person was in Honors in College? Mutually Exclusive Events:
Essential question: How do you find the probability of mutually exclusive events and overlapping events?
Two events are mutually exclusive if the events cannot both occur in the same trial of an experiment. For example, when you toss a coin, the coin landing heads up and the coin landing tails up are mutually exclusive events. Their probability is given by the formula P
(A or B) = P (A) + P (B). When the two events are non-­‐mutually exclusives, the formula is P (A or B) = P (A) + P (B) − P (A and B).
We Do: You shuffle a standard deck of playing cards and choose a card at random. What is the probability that you choose a king or a heart? A. Let event A be the event that you choose a king. Let event B be the event that you choose a heart. There are 52 cards in the deck. There are 4 kings in the deck, so P(A) = . There are 13 hearts in the deck, so P(B) = . There is one king of hearts in the deck, so P(A and B) = . B. Use the Addition Rule. P(A or B) = P(A) + P(B) − P(A and B) = + − Substitute. = or Simplify. C. So, the probability of choosing a king or a heart is Classwork (You Do): 1. A bag contains 3 blue marbles, 5 red marbles, and 4 green marbles. You choose a marble without looking. What is the probability that you choose a red marble or a green marble? 2. A bag contains 26 tiles, each with a different letter of the alphabet written on it. You choose a tile without looking. What is the probability that you choose a vowel or a letter in the word GEOMETRY? 3. You shuffle a standard deck of playing cards and choose a card at random. What is the probability that you choose a face card (jack, queen, king, or a club)? 4. You roll two number cubes at the same time. Each cube has sides numbered 1 through 6. What is the probability that the sum of the numbers rolled is even or greater than 9? 5. You have a set of 25 cards numbered 1 through 25. You shuffle the cards and choose a card at random. What is the probability that you choose a multiple of 3 or a multiple of 4? 6. A spinner is divided into 10 equal parts and numbered from 1 through 10. What is the probability of spinning a number less than 6 or greater than 6 in a single spin? 7. In a class of 160 students, there are 55 who like pizza best for dinner and 30 who like ice cream best for dessert. Find the probability that a randomly-­‐chosen student likes pizza best for dinner or ice cream best for dessert when 15 like both. 8. Of 100 students, 37 are taking Calculus, 40 are taking French, and 14 are taking both Calculus and French. If a student is picked at random, what is the probability that the student is taking Calculus or French? 9. Find the probability that a capital letter chosen at random has line symmetry or is a vowel. Use the alphabet below to check for line symmetry: A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z 10. Describe how the rule for finding P(A or B) differs when A and B are mutually exclusive and when A and B are overlapping events. Include the difference between mutually-­‐exclusive and overlapping events in your explanation. Provide an example of each type of event. EXIIT TICKET: Sam is randomly selecting a number between 1 and 50. Explain how he can determine the probability of selecting a number that is a multiple of 2 or a multiple of 5. Homework: The two-­‐way table provides data on the students at a high school. You randomly choose a student at the school. Find each probability. Freshman
Sophomore
Junior
Senior
TOTAL
Boy
98
104
100
94
396
Girl
102
106
96
108
412
TOTAL
200
210
196
202
808
a. The student is a senior. b. The student is a girl. c. The student is a senior and a girl. d. The student is a senior or a girl.