QUESTIONS
Question 1
At a major international airport, passengers are questioned about their destination. Given Events A and B, are the two events mutually exclusive? Explain your answer.
Event A: The passengers are traveling to Paris, France.
Event B: The passengers are NOT traveling to Paris, France.
Question 2
Subway trains and transit buses operate on different days and cannot occur together at the same time, even with delays. Given the following events, which of the statements is true? Select all that apply.
Event A: The subway train “X” is delayed.
Event B: The subway train “X” is on time.
Event C: The transit bus “M” is delayed.
Question 3
The event of using your free hour to nap is A and the event of using your free hour to study is B. If these events are mutually exclusive events, using P(A)=0.23, and P(B)=0.73, what is P(B|A)?
Question 4
Given the following information about events A and B:
- P(A)=1/12
- P(A AND B)=1/16
- P(A|B)=1/12
Are events A and B mutually exclusive, independent, both, or neither?
Question 5
The event the number 9 car wins the race is A and the event the number 8 car wins the race is B. If these events are mutually exclusive events, using P(A)=0.39, and P(B)=0.31, what is P(A|B)?
Question 6
Given the following information about events A and B
- P(A)=0
- P(A AND B)=0
- P(B)=0.25
Are A and B mutually exclusive, independent, both, or neither?
Question 7
Pregnant women have the option of being scanned for Cystic Fibrosis risks in their unborn babies. If a mother or a father have a certain recessive gene, the baby is at risk for Cystic Fibrosis.
Given the three events, which of the following statements is true? Select all that apply.
Event A: The mother or father carries the recessive gene.
Event B: The father carries the recessive gene.
Event C: The baby is at risk for Cystic Fibrosis.
Question 8
A student works at an on-campus job Monday through Friday. The student also participates in intramural volleyball on Tuesdays and Thursdays. Given Events A and B, are the two events mutually exclusive? Explain your answer.
Event A: On a random day of the week, the student is working at their on-campus job.
Event B: On a random day of the week, the student is playing intramural volleyball.
Question 9
The following information about undergraduates at a university is given:
- The probability that a randomly chosen undergraduate attends office hours is 24%;
- The probability that a randomly chosen undergraduate has a 30GPA or higher is 15.5%;
- The probability that a random chosen undergraduate has a 30GPA or higher given that they attend office hours is 12%.
Let event A is an undergraduate attending office hours and event B is an undergraduate having a 3.30 or higher GPA. Are events A and B mutually exclusive, independent, both, or neither?
Question 10
Given the following information, determine whether events B and C are independent, mutually exclusive, both, or neither.
- P(B)=5/6
- P(B AND C)=1/2
- P(C)=2/3
Question 11
The event of eating breakfast at a diner is A and the event of watching cable is B. If these events are independent events, using P(A)=0.22, and P(B)=0.46, what is P(B|A)?
Question 12
The event of drinking your one cup of coffee black is A and the event of drinking your one cup of coffee with milk is B. If these events are mutually exclusive events with P(A)=0.50 and P(B)=0.33, what is P(B|A)? Give your answer as an integer or a decimal.
ANSWERS:
Question 1
At a major international airport, passengers are questioned about their destination. Given Events A and B, are the two events mutually exclusive? Explain your answer.
Event A: The passengers are traveling to Paris, France.
Event B: The passengers are NOT traveling to Paris, France.
Answer:
Yes, the events are mutually exclusive because they have no outcomes in common.
Question 2
Subway trains and transit buses operate on different days and cannot occur together at the same time, even with delays. Given the following events, which of the statements is true? Select all that apply.
Event A: The subway train “X” is delayed.
Event B: The subway train “X” is on time.
Event C: The transit bus “M” is delayed.
Answer:
Event B and Event C are mutually exclusive.
Event A and Event B are mutually exclusive.
Event A and Event C are mutually exclusive.
Question 3
The event of using your free hour to nap is A and the event of using your free hour to study is B. If these events are mutually exclusive events, using P(A)=0.23, and P(B)=0.73, what is P(B|A)?
Answer:
0
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