# Bernoulli Trials / Geometric and Binomial models

1. suppose a computer chip manufacturer rejects 3% of the chips produced because they fail presale testing.

A. What is the probability that the sixth chip you test is the first bad one you find?

My Answer:

Using the Geometric Probability Model

Conditions:

1. Only 2 possible outcomes - yes

2. p is constant - yes, 0.03

3. the trials are independent or n< 10% of the population - yes

p = bad chip = 0.03

Q = good chip = 0.97

P(X) = (q^x-1)(p)

P(X=6) = (.97^5)(.03) = 0.026

B. If you test 4 chips, what is the probability that none of the chips fails?

My answer:

Using the Binomial Probability Model

(Check conditions again, all apply)

p = 0.03

q = 0.97

n = 4

k = 0

nCk = n! / (k!)(n-k)! = 4! / 0!4! = 1

P(X) = (nCk)(p^k)(q^n-k) = (1)(0.03^0)(0.97^4) = 0.885

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#### Solution Preview

I checked both your solutions and both of them are correct.

In both these problems you are dealing with a set of Bernoulli trials. You have correctly identified a single Bernoulli trial as an experiment where there are only two possible outcomes, sometimes called "success" and ...

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This solution checks and explains the anwers to questions about bernoulli trials and Geometric and Binomial probability models.