Question

an automobile manufacturer obtains the microprocessors used to regulate fuel consumption in its automobiles from three microelectronic firms: a, b, and c. the quality-control department of the company has determined that 5% of the microprocessors produced by firm a are defective, 1% of those produced by firm b are defective, and 3.5% of those produced by firm c are defective. firms a, b, and c supply 35%, 20%, and 45%, respectively, of the microprocessors used by the company. what is the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor?

Answer 1

The probability that a randomly selected automobile manufactured by the company will have a defective microprocessor is 3.525%.

Step-by-step explanation:

To find the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor, we need to consider the probabilities of getting defective microprocessors from each firm and their respective supply percentages.

Let's calculate:

Probability of getting defective microprocessors from Firm A:

= 0.05 * 0.35

= 0.0175

Probability of getting defective microprocessors from Firm B:

= 0.01 * 0.20

= 0.002

Probability of getting defective microprocessors from Firm C :

= 0.035 * 0.45

= 0.01575

Now, we add up these probabilities to get the overall probability of getting a defective microprocessor:

0.0175 + 0.002 + 0.01575

= 0.03525 or 3.525%