# 2011-11-11

```Friday 11 November 2011
Math 215 Class Record
Goal

Make connections between probability and fraction arithmetic
1. Problem from book: Spot is trained to sniff drugs. His trainers estimate that
he’ll bark at a bag without drugs 1% of the time. In suitcases with drugs he
barks 97% of the time. Suppose 1 in 10,000 suitcases have drugs in them. If
Spot barks at a suitcase, what is the probability the suitcase has drugs?
Interpret as a conditional probability question and model with the fraction
arithmetic model.
a. Suppose Spot sniffs 1,000,000 suitcases (very many!). How many have
drugs? (100)
b. How many of those with drugs does he bark at? (97)
c. How many of those without drugs does he bark at? (1% of 999,900, or
9,999).
d. How many does he bark at, and how many of those have drugs?
(10,096 and 97, respectively). What is the probability? (97/10,096 &lt;
1%!)
2. Suppose 1% of suitcases have drugs in them. Assume now Spot barks 99.9%
of the time a suitcase has drugs in them, and that he barks at a bag without
drugs .1% of the time. If Spot barks at a suitcase, what is the probability the
suitcase has drugs?
3. Show a tree diagram for this situation.