Answer the questions below (in some word processor).  Show the most important steps.  For example,

Question: What is the probability of getting three heads in a row with a fair coin?
Answer: .5*.5*.5=.125 or (1/2)*(1/2)*(1/2)=.125.

Do NOT leave your final answer as a fraction.  Instead, divide it out like the example above.
 

***********

1.  Imagine you have a trick coin that lands heads up 75% of the time and that you flip the coin 4 times.  Write out every possible outcome.  Hint 1: There are 16 possible outcomes.  Hint 2: "Head, Tail, Head, Head " or simply "HTHH" is one possible outcome.
 

2. Calculate the probability of every outcome in question 1.  Hint: They are not all equal.

3.  What do the probabilities sum to in question 2?

4. Plot the probability distribution of getting 0, 1, 2, 3, or 4 heads.  Hint 1: see the histogram in Probability lecture; your histogram won't be the same, but the example should make it clear what is being asked here.  Hint 2: Use your answer from question 2 to figure out the exact numbers.

5.  If you flipped the coin 4 times (as discussed above) 250 times (for a total of a 1000 flips), how many times would you expect to get 2 heads?  How many times would you expect to get 2 or more heads?

********************

6. If the probability of student Z getting an A on a test is .3, a B is .5, a C is .1, and a F is .1, what is the probability of student Z getting an A or a C?

7. There is a 20% chance the number 28 bus in Olympia, WA will run late. There is a 30% chance the number 5 bus in Austin will run late. These events are independent. What is the probability that both buses will run late?