1. Assume a setting in which:
For example we have identical bags of M&Ms in which each bag has exactly the same proportion of browns, say 20%. We pull one M&M from the first bag. If it is brown we say we have a success. If it is not brown we try the second bag and so on until we finally pull a brown M&M from a bag.
Fill in the chart below for the situation described above:
|
Bag # |
Probability of success on bag # |
|
1 |
P(1) = |
|
2 |
P(2) = |
|
3 |
P(3) = |
|
4 |
P(4) = |
|
k |
P(5) = |
Check your answer with your teacher.
2a. By hand, make a rough plot of the distribution you created in part 1. Give some idea of what the complete distribution will look like.
Question: Could you ever plot the entire distribution?
3. This setting is called a
Geometric Distribution. The TI-83 can calculate geometric probabilities. Confirm each of your answers in your chart in step 1 if P(4) can be found by geometpdf (0.2,4)4. Use your calculator to create a scatter plot of the first 20 elements of this Geometric Distribution. Reminder: seq(x,x,1,20,1) -> L1 places 1,2,...,20 in L1. Make a rough copy of that plot below.
5. For the problem above, what is the probability that the first brown M&M is pulled out sometime before the 23rd bag? Hint: Easy to do on the calculator. Write the command and answer below:
6. How are the binomial and the geometric settings different?
7. Challenges.
a. Without using your calculator, roughly draw a geometric distribution on your plot in step 4 which would show the likelihood of probability of pulling a brown M&M is each bag contained 70% brown M&Ms.
b. Check your answer by scatter plotting both distributions (20% brown and 70% brown) on the same graph using different symbols.