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) The probability that the first warped glass item is the 12th item produced is

              (b) The probability that the first warped item is the first, second, or third item produced is .

             (c) The probability that none of the first 10 glass items produced are defective is .

Step-by-step explanation:

From the question,

Glass manufacture found that 1 in every 1000 glass items produced is warped.

So,               P(1 in every 1000) = =

Now,

(a) Find the probability that the first warped glass item is the 12th item produced.

Here, There are occurence of data in a successive order so we use the Geometric Distribution.

Formula of Geometric Distribution =

                                                                                 (Where P is the probability)

Now,

         P(12) =

         P(12) = 0.0009890

(b) Find the probability that the first warped item is the first, second, or third item produced.

P(1) = =

P(2) =

P(3) =

Use the addition rule;

               =

              =

(c) Find the probability that none of the first 10 glass items produced are defective.

P(1) =

P(2) =

using the same formula,

P(3) =

P(4) =

P(5) =

P(6) =

P(7) =

P(8) =

P(9) =

P(10) =

Using addition rule

                  =

Using the complement rule

P(X > 10) =

              =

              =