Download Investigation: Addition Rule

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Addition Rule Investigation
Mutually Exclusive Events: Events that cannot occur at the same time.
Example: rolling a two and a three on one dice in one toss
Picking a king and queen on the same card
Of the 100 students in 12th grade, 70 are enrolled in mathematics, 50 are in science, 30 are in both subjects, and 10
are in neither subject.
Step 1: “A student takes mathematics” and “a student takes science” are two events. Are these events mutually exclusive?
Explain.
Step 2: Complete the Venn diagram to show the number of students in mathematics and science courses. Then use the
numbers of students in your Venn diagram to calculate
probabilities.
Step 3: Explain why the probability that a randomly chosen
student takes mathematics or science, P(Math or Science), does
not equal P(Math) + P(Science).
Step 5: Complete the chart to include all outcomes of rolling two dice.
The first possibility of rolling a 1 and a 1 has been done for you.
Step 6: Suppose two dice are tossed. Suppose
Event A = “sum is 7:
Event B = “each die > 2”
First Roll
Step 4: Create a formula for calculating P(Math or Science) that
includes the expressions P(Math), P(Science), and P(Math and Science).
1,1
1
Find the probabilities in parts a – e by counting the possibilities in the
chart. (A highlighter or colored pencil might be helpful.)
a. P(A)
b. P(B)
c. P(A and B)
1
2
3
4
5
6
2
3
4
5
Second Roll
d. P(A or B)
e. Find P(A or B) by using a rule or formula similar to your response in Step 4.
Step 7: Complete the statement: For any two events A and B, P(A or B) =
Kamischke, Ellen, Eric Kamischke, and Jerald Murdock, Discovering Advanced Algebra: An Investigative Approach. Emeryville: Key Curriculum, 2004. p. 681
6
Practice: First identify whether the events described are mutually exclusive. Then answer the question.
1. In a group of 101 students, 30 are freshmen and 41 are sophomores. Find the probability that a student picked from this
group at random is either a freshman or a sophomore.
2. In a group of 101 students, 40 are juniors, 50 are female, and 22 are female juniors. Find the probability that a student
picked from this group at random is either a junior or a female.
3. A single 6-sided die is rolled. What is the probability of rolling a 2 or a 5?
4. A single card is chosen at random from a standard deck of 52 playing cards. What is the probability of choosing a king or
a club?
5. In a math class of 30 students, 17 are boys and 13 are girls. On a unit test, 4 boys and 5 girls made an A grade. If a student
is chosen at random from the class, what is the probability of choosing a girl or an A student?
6. On New Year's Eve, the probability of a person having a car accident is 0.15. The probability of a person driving while
intoxicated is 0.32 and probability of a person having a car accident while intoxicated is 0.09. What is the probability of a
person driving while intoxicated or having a car accident?
7. The probability of a New York teenager owning a skateboard is 0.37, of owning a bicycle is 0.81, and of owning both is
0.36. If a New York teenager is chosen at random, what is the probability that the teenager owns a skateboard or a bicycle?
8. A single 6-sided die is rolled. What is the probability of rolling a number greater than 3 or an even number?