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 6% of the microprocessors produced by firm a are defective, 7% of those produced by firm b are defective, and 5.5% of those produced by firm c are defective. firms a, b, and c supply 45%, 30%, and 25%, 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?

The probability that a randomly selected automobile manufactured by the company will have a defective microprocessor is 6.2 %.

Step-by-step explanation:

Given:

The probability of getting a microprocessor from firm A is,

The probability of getting a microprocessor from firm B is,

The probability of getting a microprocessor from firm C is,

Now, let event D be having a defective microprocessor at random.

So, as per the question,

Probability of producing a defective microprocessor from firm A is,

Probability of producing a defective microprocessor from firm B is,

Probability of producing a defective microprocessor from firm C is,

Now, probability of having a defective microprocessor when selected at random is given as:

Therefore, the probability that a randomly selected automobile manufactured by the company will have a defective microprocessor is 6.2 %.

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step-by-step explanation: