Recognizing Mutually Exclusive Events In Exercises 1–6, decide if the events are
ID: 2930459 • Letter: R
Question
Recognizing Mutually Exclusive Events In Exercises 1–6, decide if the events are mutually exclusive. Write M (upper case) for mutually exclusive and N(upper case) for non-mutually exclusive.
1. Event A: Randomly select a female public school teacher.
Event B: Randomly select a public school teacher who is 25 years old.
2. Event A: Randomly select a member of the U.S. Congress.
Event B: Randomly select a male U.S. Senator.
3. Event A: Randomly select a student with a birthday in April.
Event B: Randomly select a student with a birthday in May.
4. Event A: Randomly select a person between 18 and 24 years old.
Event B: Randomly select a person who drives a convertible.
5. Event A: Selecting a week in which overtime wages were paid
Event B: Selecting a week in which temporary help wages were paid.
6. Event A: Selecting a week in which overtime wages were paid.
Event B: Selecting a week in which no wages were paid.
Explanation / Answer
Mutually exclusive events refer to events which do not have any element in common.
In each of the 6 cases we will try to identify if there is any element common between the 2 events.
1) Here if a female teacher is 25 years old then she will be a common element between the 2 events -> the 2 events are NOT mutually exclusive
2) Here each male member of the senate is also a member of the Congress because Senate is a subset of Congress. Hence all elements of B are common with A, Hence A and B are NOT mutually exclusive
3) Students whose birthday's are in May cannot come in B and vice-versa. Hence A and B are MUTUALLY EXCLUSIVE.
4) Here if a person between age 18 to 24 drives a convertible then that person is common to events A and B. Hence A and B are NOT mutually exclusive.
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