find indicted probabilities Find the indicated probabilities

Find the indicated probabilities using the geometric distribution or Poisson distribution. Then determine if the events are unusual. If convenient, use a Poisson probability table or technology to find the probabilities. A glass manufacturer finds that 1 in every 200 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) PCthe first warped glass item is the 12th item produced) (Round to three decimal places as needed.) (b) Pthe 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)-Q (Round to three decimal places as needed.) Which of the events are unasual? Select all that apply The event in part (a) is unusual. The event in part (b) is unusual. The event in part (c) is unusuaL B.

Solution

a)

Probability = (199/200)^11 * (1/200)^1 = 0.005 Answer

b)

Probability = 1/200 + (199/200)(1/200) + (199/200)(199/200)(1/200) = 0.015 Answer

c)

Probability = (199/200)^10 = 0.951 Answer