8. (Ch. 2.2) Consider randomly selecting a student at a large university, and le

Question

8. (Ch. 2.2) Consider randomly selecting a student at a large university, and let A be the event that the selected student has a Visa card and B be the analogous event for MasterCard. Suppose that P(A) = .7 and P(B) = .3. (a) Could it be the case that P(An B).5? Explain why or why not. (b) Now suppose P(An B-2. what is the probability that the selected student has at least one of the two types of cards? c) What is the probability that the selected student has neither type of card? (d) Consider the event that the selected student has a Visa but not a MasterCard. Write this event in terms of A and B using set operations, and calculate the probability of this event. (e) Calculate the probability that the selected student has exactly one of the two types of cards.

Explanation / Answer

a) no,

P(A and B) can not be more than P(B)

b)

P( A or B) = (P(A) + P(B) - P(A and B))

= 0.7 + 0.3 - 0.2 = 0.8

c)

1 - P(A or B) = 1 - 0.8 = 0.2

d)

A - B

P(A -B) = P(A) - P(A and B) = 0.7 - 0.2 = 0.5

e)

P(A -B) + P(B -A)

= P(A) + P(B) - 2* P(A and B)

= 0.7 +0.3 - 2* 0.2

= 0.6

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