Question

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?

Answer 1

Answer:

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