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