Question 1
The personal identification numbers (PINs) for automatic teller machines usually
consist of four digits. You notice that most of your PINs have at least one 0, and you wonder
if the issuers use lots of 0s to make the numbers easy to remember. Suppose that PINs are
assigned at random, so that all four-digit numbers are equally likely.
(a) How many possible PINs are there?
(b) What is the probability that a PIN assigned at random has at least one 0?
(c) What is the probability that a PIN assigned at random has at least two 0?
Question 2
…For the rapid HIV tests, the Food and Drug Administration (FDA) has established 2% as the maximum false positive rate for a rapid HIV test. If a clinic uses a test that meets the FDA standard and tests 50 people who are free of HIV antibodies,
(a) What is the probability that at least one false-positive will occur?
(b) What is the probability that at least two false-positive will occur?
✅ Answers
? Best Answer
b) 10^4 – (no 0) = 10^4 – 9*9*9*9 = 3439
3439/10000 = 0.3439
c) 10^4 – (no 0 or one 0) = 10^4 – 9*9*9*9 – 1*9*9*9*4 = 523
523/10000 = 0.0523
50 people are tested, 2% false positive rate. 1 person out of 50 is allowed to be diagnosed incorrect.
a) the test will show: either 0 or 1 false-positive, so the probability is 0.5 (no guarantee, may be wrong)
b) at least 2 false-positive means at least 4% false rate, this no longer meets the FDA standard, so this will never occur because we are told that “clinic uses a test that meets FDA standard”. Probability is 0.