Question

An aircraft seam requires 20 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 16% of all seams need reworking, what is the probability that a rivet is defective

Answer 1

probability that a rivet is defective is 0.00868

Explanation:

given data

rivets = 20

all seam need reworking P = 16% = 0.16

solution

we consider here probability of a defective rivet = p

and 0.16 = P [Seam needs reworking) = P (at least one rivet in the seam is defective)

so that for non-defective = 1 - P [all the rivets are non-defective]

and that will be here as = 1 - P [rivet 1 is non-defective, rivet 2 is non-defective, rivet 3 is non-defective,...............,rivet 20 is non-defective]

=
`1 - (p})^(20)` ....................1

so

1-0.16 =
`1 - (p})^(20)`

0.84 =
`1 - (p})^(20)`

`0.84^{(1)/(20)}` = 1 - p

solve it we get

p = 0.00868

so, probability that a rivet is defective is 0.00868