Question

A manufacturer of motorcycle parts guarantees that a box of 24 parts will contain at most 3
defective parts. If the records show that the manufacturer’s machines produce 2% defective parts,
what is the probability that a box of parts will satisfy the guarantee?

Answer 1

Answer:

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Answer 2

Concept

Probability is defined as the certainty of occurrence of the event out of all the possible outcomes.

Given

A box will contain at most 3 defective pieces out of 24 parts.

Find

Probability that box of parts will satisfy the guarantee.

Solution

Let P(x=i) be the probability of i defective parts in box.

P(satisfies the guarantee) = P(X=0) +P(X=1) +P(X=2) +P(X=3)

P(X=0) = 0.98^24

P(X=1)= 24C1 x 0.98^23x0.02

P(X=2)= 24C2 x 0.98^22  x 0.02^2

P(X=3) = 24C3 x 0.98^21x0.02^3

Hence adding all we get ,

P(X=0) +P(X=1) +P(X=2) +P(X=3)

= 0.98^24+24C1 x 0.98^23x0.02 +24C2 x 0.98^22 x 0.02^224C3 x 0.98^21x0.02^3

=0.999

Hence , the probability that a box of parts will satisfy the guarantee is 0.999

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