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 0.40 0.03 0.07 6Cylinder 0.34 0.08 0.08

Answer 1

The table is as follows :

	Octane-87	Octane-90	Octane-92
4-cylinder	0.40	0.03	0.07
6-cylinder	0.34	0.08	0.08

Now, we have to find the probability of purchasing a 6-Cylinder engine car given that the car uses Octane-90 gas.

P(the car uses octane-90 gas) = 0.03 + 0.08 = 0.11

P( purchases a 6-Cylinder engine car and the car uses Octane-90 gas) = 0.08

Therefore, P(purchasing a 6-Cylinder engine car given that the car uses Octane-90 gas) = 0.08 / 0.11

=0.727

Now,we have to find the probability of purchasing a car that uses Octane-92 gas given it has a 4-Cylinder engine.

P(the car has a 4-cylinder engine) = 0.40 + 0.03 + 0.07 = 0.50

P(purchasing a car that uses Octane-92 gas and it has a 4-Cylinder engine) = 0.07

Therefore , P(purchasing a car that uses Octane-92 gas given it has a 4-Cylinder engine) = 0.07 / 0.50

= 0.14

Now, we have to find the probability of purchasing a car that uses Octane-90 or higher given that it has a 6-Cylinder engine.

P(the car has a 6-cylinder engine) = 0.34 + 0.08 + 0.08 = 0.5

P(purchasing a car that uses Octane-90 or higher and it has a 6-Cylinder engine) = 0.08 + 0.08 = 0.16

Therefore , P(purchasing a car that uses Octane-90 or higher given that it has a 6-Cylinder engine) = 0.16 / 0.5

= 0.32