An aircraft seam requires 27 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability. (Round your answers to four decimal places.) (a) If 25% of all seams need reworking, what is the probability that a

This question is incomplete, the complete question is;

An aircraft seam requires 27 rivets. The seam will have to be reworked if any of these rivets is defective. Suppose rivets are defective independently of one another, each with the same probability. (Round your answers to four decimal places.)

If 25% of all seams need reworking, what is the probability that a rivet is defective?

the probability that a rivet is defective is  0.0106

Step-by-step explanation:

Given the data in the question,

let event X represent seam fails and event B represent rivet fails.

now, 25% of all seams need reworking;

i.e P(X) = 25% = 0.25

the probability that a rivet is defective will be;

P( A ) = 1 - P( B' )²⁷

so

0.25 = 1 - P( B' )²⁷

P( B' )²⁷  = 1 - 0.25

P( B' )²⁷  = 0.75

P( B' ) =  

P( B' ) = 0.9894

so

P( B ) = 1 - 0.9894

P( B ) = 0.0106

Therefore, the probability that a rivet is defective is  0.0106