Question

Do part e f and g please

3. A certain auto mall sells only Fords, Hondas, and Toyotas. Each customer buys only 1 car It is known that 45% of all customers buy a Toyota and 35% buy a Ford. It is also known that 40% of the Toyota customers buy a white car whereas only 30% of the Honda customers buy a white car. None of the Ford customers buy a white car a. Express all numbers given in the problem statement as probabilities of events. (2 pts) b. What is the probability that the customer bought a white car? (2 pts) c. If the customer bought a white car, what is the probability that he or she bought a Toyota? (2 pts) It is observed that 65% of all customers buy an automatic shift car. However, 80% of white Tovota buvers purchase an automatic shift d. What is the probability that the customer buys a white Toyota with an automatic shift? (2 pts) What is the probability that the customer bought a white Toyota given that he or she bought an automatic shift car? (2 pts) e. Draw Venn diagrams and express in set notation the events that f. A customer buys a white Toyota with manual (non-automatic) transmission. (2 pts) g. A customer buys either a non-white Honda or a Ford with automatic transmission. (2 pts)

Answer 1

Bayes' Theorem: P(A | B) = P(A & B)/P(B)

e) P(white Toyota | automatic shift car) = P(white Toyota and automatic shift) / P(automatic shift)

= (0.45x0.4x0.8)/0.65

= 0.2215

Let T indicates that a car is Toyota, H indicate Honda and F indicate Ford. Also, Let W indicate that a car is white and A indicate that its having Automatic shift.

f) White Toyota with Manual transmission = W $\cap$ T $\cap$ A'

Venn Diagram

g) Either a non-white Honda or a Ford with Automatic transmission

= (H $\cap$ W') U (F $\cap$ A)

Venn Diagram