Question 1

Scenario: Consider randomly selecting a student at a large university and asking them what type of card they have.

Events:

  • - Student has a Visa card.
  • - Student has a MasterCard.

Probabilities:

  • .
  • .

(a)

Question: Could it be the case that ? Why or why not?

Answer: No, this is not possible. Since is contained in the event , it must be the case that . However, violates this requirement.

Summary

(b)

Question: From now on, suppose that . What is the probability that the selected student has at least one of these two types of cards?

Process: The phrase "... at least one of these two types of cards" indicates we're finding the probability of the events in and/or the events in occurring. That's equivalent to the union (or) of the events in and .

Answer: 0.9.

Summary

The probability of a selected object belonging to either or is:

(c)

Question: What is the probability that the selected student has neither type of card?

Process: The phrase "neither type of card" indicates we're finding the probability of none of the events in or . That's equivalent to the complement of the union between the events in and .

Answer: 0.1.

Summary

The probability of a selected object not belonging to neither nor is:

(d)

Question: Describe, in terms of and , the event that the selected student has a Visa card but not a MasterCard.

Process: The phrase "has a Visa card but not a MasterCard" indicates we're only interested in the events of and the events not in . This is expressed as the intersection (and) of the events in and the complement of .

Answer: .

(e)

Question: Calculate the probability that the selected student has exactly one of the two types of cards.

Process: The phrase "has exactly one of the two types of cards" indicates we're finding the probability of all events in and none in in addition to all events in and none in .

Answer: 0.7.

Summary

The probability of a selected object belonging to only or only is: