Find the indicated probabilities using the geometric​ distribution, the Poisson​ distribution, or the binomial distribution. Then determine if the events are unusual. If​ convenient, use the appropriate probability table or technology to find the probabilities.
A glass manufacturer finds that 1 in every 500 glass items produced is warped. Find the probability that​ (a) the first warped glass item is the 12th item​ produced, (b) the first warped item is the​ first, second, or third item​ produced, and​ (c) none of the first 10 glass items produced are defective.
​(a) P(the first warped glass item is the 12th item ​produced)=
​(Round to three decimal places as​ needed.)
​ (b) P(the first warped item is the​ first, second, or third item ​produced)=
​(Round to three decimal places as​ needed.)
​ (c) P(none of the first 10 glass items produced are ​defective)=
​(Round to three decimal places as​ needed.)
Which of the events are​ unusual? Select all that apply.
A. The event in part​ (a) is unusual.
B. The event in part​ (b) is unusual.
C. The event in part​ (c) is unusual.
D. None of the events are unusual.