Find the indicated probabilities using the geometric distribution, the Poisson d

Question

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 1000 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) =

b) P(the first warped item is the first, second, or third item produced) =

(c) P(none of the first 10 glass items produced are defective) =

Which of the events are unusual?

Explanation / Answer

Here P(warped) = 1/1000 = 0.001

(a) P(the first warped glass item is the 12th item produced) = It wil be solved by geometric distribution. THat means in initially 11 chances there are no warped item and in 12th chance, there is a warp item.

P(the first warped glass item is the 12th item produced) = (0.999)11 (0.001) = 9.89 * 10-4

(b) P(the first warped item is the first, second, or third item produced) = P(1) + P(2) + P(3)

= 0.001 + 0.999 * 0.001 + 0.9992 * 0.001 = 0.003

(c) P(none of the first 10 glass items produced are defective) = initially none of 10 glasses are warped

= 10C0 * (0.999)10 = 0.99

Here event a is unusual that first warped glass item is the 12th item produced

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