Answer:
b) 0.2464
c) 0.0580
d) 0.2952
Step-by-step explanation:
Probability of those that purchased regular gas = 88% = 0.88
2% purchased mid grade gas
10% purchased premium gad
Given that a driver bought regular gas, 28% paid with credit card
Given that a driver bought mid grade gas, 34% paid with credit card
Given that a driver bought premium gas, 42% paid with credit card
Let R represent drivers that bought regular gas
Let M represent drivers that bought mid grade gas
Let P represent drivers that bought premium gas
Let C represent credit card payment
Let NC represent non-credit card payment
Pr(R) = 88% = 0.88
Pr(M) = 2% = 0.02
Pr(P) = 10% = 0.10
Pr(C|R) = 28%= 0.28
Pr(C|M) = 34%= 0.34
Pr(C|P) = 42%= 0.42
Pr(NC|R) = 1 - 0.28= 0.72
Pr(NC|M) = 1 - 0.34 = 0.66
Pr(NC|P) = 1 - 0.42 = 0.58
Using multiplication rule
Pr(AnB) = Pr(A) * Pr(B|A) = Pr(B) * Pr(A|B)
Using conditional probability,
P(B|A) = Pr(AnB) / Pr(A)
Pr(CnR) = Pr(R) * Pr(C|R)
= 0.88*0.28
= 0.2464
Pr(CnM) = Pr(M) * Pr(C|M)
= 0.02*0.34
= 0.0068
Pr(CnP) = Pr(P) * Pr(C|P)
= 0.10*0.42
= 0.0420
b) the probability that an automobile driver filled with regular gasoline AND paid with a credit card =
Pr(CnR)
= 0.2464
c) the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card = Pr(P n NC) = Pr(NC|P) * Pr(P)
= 0.58 * 0.10
= 0.0580
d) The probability of those that paid with credit card is given as
Pr(CnR) + Pr(CnM) + Pr(CnP)
= 0.2464 + 0.0068 + 0.042
= 0.2952
