SOLUTION: A new sports car model has defective brakes 8 percent of the time and a defective steering mechanism 4 percent of the time. Let’s assume (and hope) that these problems occur inde

Question 1183236: A new sports car model has defective brakes 8 percent of the time and a defective steering mechanism 4 percent of the time. Let’s assume (and hope) that these problems occur independently. If one or the other of these problems is present, the car is called a “lemon.” If both of these problems are present, the car is a “hazard.” Your instructor purchased one of these cars yesterday. What is the probability it is a “lemon?”
Answer by ikleyn(52866) (Show Source): You can put this solution on YOUR website!
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A new sports car model has defective brakes 8 percent of the time and a defective steering mechanism 4 percent of the time.
Let’s assume (and hope) that these problems occur independently.
If one or the other of these problems is present, the car is called a “lemon.”
If both of these problems are present, the car is a “hazard.”
Your instructor purchased one of these cars yesterday. What is the probability it is a “lemon?”
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P(both) = 0.08*0.04 = 0.0032.


P(lemon) = P(brakes are defective, steering is OK) + P(brakes are OK, steering is defective) = 

         = (0.08 - 0.0032) + (0.04-0.0032) = 0.1136 = 11.36%.    ANSWER

Solved and explained.

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