University:
High School
Course:
High School Mathematics
Academic year:

2022
Views:

411

Pages:

5
Author:

kampeini14yb

Essential Question: How can you find probabilities of disjoint and overlapping events? Two events are disjoint, or mutually exclusive, when they have no outcomes in common. Two events are overlapping when they have one or more outcomes in common. 1 EXPLORATION: Disjoint Events and Overlapping Events Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Work with a partner. A six-sided die is rolled. Draw a Venn diagram that relates the two events. Then decide whether the events are disjoint or overlapping. a. Event A: The result is an even number. Event B: The result is a prime number. [Venn diagram with two overlapping circles. Circle A labeled "Even" contains 2, 4, and 6. Circle B labeled "Prime" contains 2, 3, and 5. The overlapping region contains 2.] overlapping b. Event A: The result is 2 or 4. Event B: The result is an odd number. [Venn diagram with two non-overlapping circles. Circle A labeled "2 or 4" contains 2 and 4. Circle B labeled "Odd" contains 1, 3, and 5.] Disjoint 2 EXPLORATION: Finding the Probability that Two Events Occur Work with a partner. A six-sided die is rolled. For each pair of events, find (a) P(A), (b) P(B), (c) P(A and B), and (d) P(A or B). a. Event A: The result is an even number. Event B: The result is a prime number. P(even) = 3/6 = 1/2 P(prime) = 3/6 = 1/2 P(even and prime) = 1/6 P(even or prime) = 5/6 b. Event A: The result is 2 or 4. Event B: The result is an odd number. P(2 or 4) = 2/6 = 1/3 P(odd) = 3/6 = 1/2 P(2 or 4 and odd) = 0/6 = 0 P(2 or 4 or odd) = 5/6 298 Algebra 2 3 EXPLORATION: Discovering Probability Formulas Go to BigIdeasMath.com for an interactive tool to investigate this exploration. Work with a partner. a. In general, if event A and event B are disjoint, then what is the probability that event A or event B will occur? Use a Venn diagram to justify your conclusion. [Venn diagram with two non-overlapping circles. Circle A and Circle B.] P(A or B) = P(A) + P(B) b. In general, if event A and event B are overlapping, then what is the probability that event A or event B will occur? Use a Venn diagram to justify your conclusion. [Venn diagram with two overlapping circles. Circle A and Circle B with an overlapping region.] P(A or B) = P(A) + P(B) - P(A and B) c. Conduct an experiment using a six-sided die. Roll the die 50 times and record the results. Then use the results to find the probabilities described in Exploration 2. How closely do your experimental probabilities compare to the theoretical probabilities you found in Exploration 2? Communicate Your Answer 4. How can you find probabilities of disjoint and overlapping events? 5. Give examples of each (not dice)