GG413 Geological Data Analysis, Fall 2014
Homework #2: Probability Basics
Read 1.4 of Wessel
Due Tuesday Sept 9
As usual please be as thorough in explaining your thought process in solving each problem below.
1) Theoretically speaking, how many distinct telephone numbers that can be accommodated in a
single area code (e.g., 808)?
2) You are a head in a company prospecting for geothermal resources in Iceland. Prior experience
tells you that the probability of drilling a single hole and having it become profitable is 10%.
(a) Say you decide to drill 2 holes no matter what the outcome is. Estimate the probability that
you will have at least 1 (i.e., 1 or 2) productive well.
(b) If you drill 3 holes, estimate the probability that you will have at least 1 (i.e., 1, 2, or 3)
productive well.
(c) If you drill 4 holes, estimate the probability that you will have at least 1 productive well.
(d) Since you want to minimize your cost (i.e., drill the fewest holes) to have a least one profitable
well, use your answers to (a)-(c) to decide on how many holes to drill.
3) Returning from extensive fieldwork in the Brazilian jungle, a biologist calmly discovers that
the glue holding the labels onto her glass specimen jars with spiders has dissolved and all the
labels have gotten separated from their corresponding jars. Of a total of 28 specimens, 8 are
previously unknown species; the remaining 20 are known to be harmless to humans. But again
all of the specimens are mixed up and the technician working on them has no idea which of the
28 is which. Given past experience that half of newly discovered spiders are poisonous, what is
the probability that, when the technician randomly selects 4 specimens,
(a) One of the specimens is a poisonous spider?
(b) all 4 are harmless?
(c) all 4 are poisonous?
4) A meat processing plant produces ground beef from three conventional industrial farms. Farm
A produces 55% of the beef for the plant, farm B 30%, and farm C 15%. Due to the overcrowded and unsanitary conditions in these mass-production farms, a percentage of the beef is
tainted with E. Coli bacteria, which can make someone really sick if the meat is not properly
cooked. The percentages of tainted beef from farm A, B, and C are 0.4%, 0.6 %, and 1.2%,
respectively.
(a) If your neighbor’s conventional ground beef comes from this meat plant, what is the
probability that the package of beef in her refrigerator is contaminated?
(b) If your neighbor discovers that her beef is indeed contaminated, which farm is most likely to
have produced the beef? (i.e., which farm has the highest probability of producing the beef
given that it is contaminated?)