1.  A basketball player hits 45% of his free-throws.   Suppose that in the course of one game he shoots 10 free-throws.  Assume that his success on one throw is independent of success or failure on any other throw.
a)  What's the experimental expected number of free-throws?  Write out the five steps of a simulation, justifying steps where appropriate.  If you can carry this out, do so.  Use at least 25 trials.
b) What's the sample space for the number of free throws he makes?
c) What's the experimental probability that he will make 6 free-throws?  What's the experimental probability that he will make at least 1?  Write out the five steps of a simulation, justifying the steps where appropriate.   If you can, carry these simulations out, using at least 25 trials.
d) What's the theoretical probability that he will make 6?  At least 1?

2.  A "combination" lock is a dial that consists of 60 numbers.  To unlock the lock, you must dial in 3 numbers in a particular order.
a) What's the probability that if you randomly dial in 3 numbers, you will open the lock?
b) Suppose that the locks are set up so that you cannot dial in the same number twice.  (So it is somehow impossible to have repeats.)  Now what's the probability of opening  the lock with a random selection?
c)  These combination locks should more appropriately be called "permutation" locks.  Why?

3.  Suppose 25% of a certain city's residents are African-American.  A jury consists of 7 people, and suppose that these people are chosen (a) independtly and (b) without regards to race or ethnicity.   One defendant suspects there is racial discrimination at play because her jury consists of no African-Americans.  Under the assumptions (a) and (b), how likely is this to happen?

4.  Suppose you toss a fair coin until the first head appears.
a) Write a formula that expressed the probability that you will get the first head on the xth flip.  (Express the formula in terms of x.)  Hint:  Begin by making a table.  What's the probability of this happening if x=1?  x=2? x=3?
b) Now assume that the coin has been tampered with so that it falls on "Heads" with probability p.  Now what's the formula?
c) The theoretical expected value is for the number of tosses before the first head is 1/p.  Do a simulation with a coin, but instead of "flipping" the coin, spin it and wait for it to fall. Do 25 trials.  What's the experimental expected number of tosses until the first head?  How close is this to the theoretical expected value?

5. Return to the Old Faithful data.  Is there a relationship between the length of an eruption of the geyser and the time until the next eruption?
a) Make a scatterplot to see if the length of the eruption can be used to predict the time until the next eruption.
b) Find the regression line.
c) Interpret the regression line.
d) Evaluate the fit of the regression line.

6.  There are two jars on a table.  One contains 6 black marbles and 4 white marbles.  The other contains 5 black marbles and 5 white marbles.  I've drawn out 25 marbles with replacement.  I got 16 blacks.  Which jar do you think I drew from and why?  Support your answer with a simulation.

STM:, p. 240, 1,2.