In the field of quality control, the science of statistics is often used to determine if a process is "out of control." Suppose the process is, indeed, out of control and 15 % of items produced are defective. (a) If two items arrive off the process line in succession, what is the probability that both are defective? (b) If three items arrive in succession, what is the probability that two are defective?

Question

Esmeralda

Mathematics

14 May, 10:14

In the field of quality control, the science of statistics is often used to determine if a process is "out of control." Suppose the process is, indeed, out of control and 15 % of items produced are defective. (a) If two items arrive off the process line in succession, what is the probability that both are defective? (b) If three items arrive in succession, what is the probability that two are defective?

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Answers (1)

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Megan Caldwell · Answer 1

a) P=0.0225

b) P=0.057375

Step-by-step explanation:

From exercise we have that 15 % of items produced are defective, we conclude that probabiity:

P=15/100

P=0.15

a) We calculate the probabiity that two items are defective:

P = 0.15 · 0.15

P=0.0225

b) We calculate the probabiity that two of three items are defective:

P={3}_C_{2} · 0.85 · 0.15 · 0.15

P=/frac{3!}{2! (3-2) !} · 0.019125

P=3 · 0.019125

P=0.057375