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 500 glass items produced is warped. find the probability that (a) the first warped glass item is the 10th 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 10th item produced) = 0.002
(round to three decimal places as needed.)

(b) p(the first warped item is the first, second, or third item produced) = 0.006
(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.)

Explanation:

Identify the probability of a single item being defective

$$ p = \frac{1}{500} = 0.002 $$

Calculate the probability that none of the first 10 items are defective

$$
LATEXBLOCK0
$$

Round the result to three decimal places

$$ P(\text{none of the first 10 are defective}) \approx 0.980 $$

Answer:

(c) P(none of the first 10 glass items produced are defective) = <blank>0.980</blank>
(Round to three decimal places as needed.)