Consider randomly selecting a student at a certain university, Let A denote the

Question

Consider randomly selecting a student at a certain university, Let A denote the event the has a Visa credit card and B be the analogous event for a MasterCard. 0.5. Suppose that P(A) = 0.6. P(B) = 0.8, and P(AOB) Are the events A, B positively or negatively dependent? If the randomly selected student admits to having a MasterCard, what is the probability that student also has a Visa card? or P(AB) If the randomly selected student denies having a MasterCard, what is the probability that student also denies having a Visa card? or PA B) a. b. c. of probability, the student has a MasterCard? P (BI UB) Note: B (A B) or

Explanation / Answer

a. P(A|B) = P(A intersect B) / P( B) = .5/.8 = 5/8

P(A|Bc) = P( A intersect Bc) / P(Bc) = .1/.2 = 1/2

If P(A|B) > P(A|Bc) then A and B are positively dependent

If P(A|B) < P(A|Bc) then A and B are negatively dependent

Since P(A|B) > P(A|Bc) , A and B are positively dependent

b. P(A|B) = P(A intersect B) / P( B) = .5/.8 = 5/8

c. P(Ac|Bc) = P(Ac intersect Bc) / P(Bc) = .1/.2 = 1/2

d. P(B | A union B) = P( B intersect AunionB) / P(A union B) = P(B) / P(A union B) = .8/.9 = 8/9

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