Name
Date
Period
Tree Diagrams and the General Multiplication Rule
Suppose that 5% of current NFL players are using steroids or other performance-enhancing
drugs (PEDs). Unfortunately, the tests used to detect PEDs aren’t perfect. Suppose that 3% of
players who are not using PEDs will test positive and consequently be accused of using PEDs,
while 1% of players who are using PEDs will test negative and escape detection.
1) Suppose that we randomly select one NFL player for testing. Find the following probabilities:
a) (
)
b) (
c) (
d) (
)
|
)
|
)
2) Display the information using a tree diagram. Then use the general multiplication rule to
calculate the probabilities of the four possible outcomes.
3) Calculate the probability that a randomly selected player will test positive.
4) If you randomly selected a player who tests positive, what is the probability that he actually
uses PEDs?