Question

The following table lists the purchase probabilities of cars corresponding to their type of engine (4-Cylinder or 6-Cylinder) and Octane rating (87, 90, 92). Use the table to answer the following: What is the probability of purchasing a 6-Cylinder engine car given that the car uses Octane-90 gas? What is the probability of purchasing a car that uses Octane-92 gas given it has a 4-Cylinder engine? What is the probability of purchasing a car that uses Octane-90 or higher given that it has a 6-Cylinder engine? O87 O90 O92 4Cylinder 0.50 0.03 0.03 6Cylinder 0.34 0.02 0.08

Answer 1

	O87	O90	O92	Total
4-Cylinder	0.5	0.03	0.03	0.56
6-Cylinder	0.34	0.02	0.08	0.44
Total	0.84	0.05	0.11	1

a.

P(purchasing a 6-Cylinder engine car given that the car uses Octane-90 gas)

=P(6-Cylinder engine intersection O90 gas )/P(O90 gas)

=0.02/0.05

=0.4

b.

P(purchasing a car that uses Octane-92 gas given it has a 4-Cylinder engine)

=P(Octane-92 gas INtersection 4-Cylinder engine )/ P(4-Cylinder engine)

=0.03/0.56

=0.05357

c.

P(purchasing a car that uses Octane-90 or higher given that it has a 6-Cylinder engine)

=P((Otane 90 or Highger) And 6 cylinder) / P(6 cylinder Engine)

=P(Otane 90 And 6 cylinder) / P( 6 cylinder) +  P(Otane 92 And 6 cylinder) /P( 6 cylinder)

= 0.02/0.44 + 0.08/0.44

=0.22727