Question: Items produced in assembly line A are defect free with probability 0.9, and those produced in assembly line B are defect free with probability 0.99. A sample of 200 items from line A and a sample of 1000 from line B are inspected.

(a) Give an approximation to the probability that the total number of defective items found is at most 35. (Hint. See Example)

(b) Use R commands similar to those used in Example to find the exact probability of part (a).

Example: A college basketball team plays 30 regular season games, 16 of which are against class A teams and 14 are against class B teams. The probability that the team will win a game is 0.4 if the team plays against a class A team and 0.6 if the team plays against a class B team. Assuming that the results of different games are independent, approximate the probability that

(a) the team will win at least 18 games, and

(b) the number of wins against class B teams is smaller than that against class A teams.