Consider randomly selecting a student at a certain universit

Consider randomly selecting a student at a certain university, and let A denote the event that the selected individual has a Visa credit card and B be the analogous event for a MasterCard where

P(A) = 0.55, P(B) = 0.40, and P(A B) = 0.20. Calculate and interpret each of the following probabilities (a Venn diagram might help). (Round your answers to four decimal places.)

(a)    P(B | A)


(b)    P(B\' | A)


(c)    P(A | B)


(d)    P(A\' | B)


(e) Given that the selected individual has at least one card, what is the probability that he or she has a Visa Card?

Solution

(a)P(B | A)=P(BnA)/P(A)

from the above information we get P(A) = 0.55, P(B) = 0.40, and P(A B) = 0.20.

P(B | A) = .20/.30=0.3636

(b) P(B\' | A) =P(B\'nA)/P(A)

using venn diagram to get P(B\'nA)=P(A) -P(AnB)=.55-.20=.35

P(B\' | A) = .35/.55=.6363

(c) P(A | B)=P(AnB)/P(B)

P(A | B)= .20/.40=0.5

(d) P(A\' | B) =P(A\'nB)/P(B)

using venn diagram to get P(A\'nB)=P(B) -P(AnB)=.40-.20=.20

P(A\' | B) = .20/.40=.5


(e) Given that the selected individual has at least one card, what is the probability that he or she has a Visa Card?

p(AuB)=P(A)+P(B)-P(AnB)=.55+.40-.20=.75

the probability that he or she has a Visa Card= .55 / .75 =.7333