Question

A manufacturing firm just received a shipment of 54 assembly parts, of slightly varied sizes, from a vendor. The manager knows that there are only 38 parts in the shipment that would be suitable. He examines these parts one at a time. a. Find the probability that the first part is suitable. (Round your answer to 2 decimal places.) b. If the first part is suitable, find the probability that the second part is also suitable. (Round your answer to 4 decimal places.) c. If the first part is suitable, find the probability that the second part is not suitable. (Round your answer to 4 decimal places.)

Answer 1

a) 70.37%

b) 69.81%

c) 30.19%

Explanation:

a)

If there are 38 suitable parts among 54, there is a probability of 38/54 = 0.7037 = 70.37% of choosing a suitable part.

b)

If the first part was suitable, then now there are 37 suitable parts among 53, so the probability of selecting a new suitable part is

37/53 = 0.6981 = 69.81%

c)

If the first part is suitable, there are 37 suitable parts in 53 parts, so there are 16 unsuitable parts, and the probability that the second part is not suitable is 16/53 = 0.3019 = 30.19%