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DarcieMATHlin819
19.09.2019 •
Mathematics
The screens used for a certain type of cell phone are manufactured by 3 companies, a, b, and c. the proportions of screens supplied by a, b, and c are 0.5, 0.3, and 0.2, respectively, and their screens are defective with probabilities 0.01, 0.02, and 0.03, respectively. given that the screen on such a phone is defective, what is the probability that company a manufactured it?
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Ответ:
The probability is 0.2941
Step-by-step explanation:
Let's call A the event that company A manufactured the screen, B the event that company B manufactured the screen, C the event that the company C manufactured the screen and D the event that the screen is defective.
The probability P(A/D) that the company A manufactures the screen given that is defective is:
P(A/D) = P(A∩D)/P(D)
Where P(D) = P(A∩D) + P(B∩D) + P(C∩D)
So, the probability P(A∩D) that the screen is manufactured by company A and the screen is defective is calculated as:
P(A∩D) = 0.5 * 0.01 = 0.005
Where 0.5 is the proportion of screens manufactured by company A and 0.01 is the probability of defective screens for screens that are manufactured by company A.
At the same way, the probability P(B∩D) that the screen is manufactured by company B and the screen is defective and the probability P(C∩D) that the screen is manufactured by company B and the screen is defective are calculated as:
P(B∩D) = 0.3 * 0.02 = 0.006
P(C∩D) = 0.2 * 0.03 = 0.006
Then, The probability P(D) that the screen is defective is equal to:
P(D) = 0.005 + 0.006 + 0.006 = 0.017
Finally, P(A/D)that the company A manufactures the screen given that is defective is:
P(A/D) = 0.005/0.017 = 0.2941
Ответ:
1/44
Step-by-step explanation: