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svetlana [45]
3 years ago
13

An automobile manufacturer obtains the microprocessors used to regulate fuel consumption in its automobiles from three microelec

tronic 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?
Mathematics
1 answer:
Anastaziya [24]3 years ago
5 0

Answer:

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, P(A)=45\%=0.45

The probability of getting a microprocessor from firm B is, P(B)=30\%=0.30

The probability of getting a microprocessor from firm C is, P(C)=25\%=0.25

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, P(D/A)=6\%=0.06

Probability of producing a defective microprocessor from firm B is, P(D/B)=7\%=0.07

Probability of producing a defective microprocessor from firm C is, P(D/C)=5.5\%=0.055

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

P(D)=P(A)\cdot P(D/A)+P(B)\cdot P(D/B)+P(C)\cdot P(D/C)\\P(D)=(0.45\times 0.06)+(0.30\times 0.07)+(0.25\times 0.055)\\P(D)=0.027+0.021+0.01375\\P(D)=0.06175\ or\ P(D)=0.06175\times 100\approx 6.2\%

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

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