probability and stimulation

Question

Ten percent of the keyboards a computer

company manufactures are defective.

Design and describe a simulation that will

determine the experimental probability that

one or more of the next three keyboards to

come off the assembly line will be

defective.

Answer 1

More likely, this company is about to go out of business, that might skew the probability of HAVING three more keyboards ....

-- Cheers, --Mr. d.

Answer 2

It seems like we have to use the binomial distribution for this scenario. We are basically looking for the number of successes and in this case, a success is when a keyboard is defective. We can denote p= 0.10. We are asked to look for the probability that 1 or more keyboard is defective, or P(X=>1).

Formula of binomial distribution: P(x) = C(n,x) * p^x * (1 - p)^n-x

The easiest way to go about this would be to rewrite what we're looking for, so P(X=>1) = 1 - P(X < 1). Because the binomial distribution is discrete, P(X < 1) = P (X = 0). Plugging in the numbers accordingly, we get:

P(X = 0) = C(3,0) * (0.10)⁰ * (0.90)³ = 0.729

To finish the problem, we do P(X => 1) = 1 - 0.729 = 0.271

There is a 27.1% chance that the next 3 keyboards will be defective.