MATH SOLVE

1 month ago

Q:
# In a recent month, 88% of automobile drivers filled their vehicles with regular gasoline, 2% purchased midgrade gas, and 10% bought premium gas. Given that a driver bought regular gas, 28% paid with a credit card; given that they bought midgrade and premium gas, 34% and 42% respectively, paid with a credit card. Suppose we select a customer at random. a. Draw a tree diagram to represent this situation. b. What is the probability that an automobile driver filled with regular gasoline AND paid with a credit card? c. What is the probability that an automobile driver filled with premium gasoline AND did NOT pay with a credit card? d. What’s the probability that the customer paid with a credit card?

Accepted Solution

A:

Answer:b) 0.2464c) 0.0580d) 0.2952Step-by-step explanation:Probability of those that purchased regular gas = 88% = 0.882% purchased mid grade gas10% purchased premium gadGiven 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 gasLet M represent drivers that bought mid grade gasLet P represent drivers that bought premium gasLet C represent credit card payment Let NC represent non-credit card payment Pr(R) = 88% = 0.88Pr(M) = 2% = 0.02Pr(P) = 10% = 0.10Pr(C|R) = 28%= 0.28Pr(C|M) = 34%= 0.34Pr(C|P) = 42%= 0.42Pr(NC|R) = 1 - 0.28= 0.72Pr(NC|M) = 1 - 0.34 = 0.66Pr(NC|P) = 1 - 0.42 = 0.58Using multiplication rulePr(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 = 0.0420b) the probability that an automobile driver filled with regular gasoline AND paid with a credit card = Pr(CnR) = 0.2464c) 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 = 0.0580d) 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