The following assignment will allow you to master the concepts you have learned on discrete probability distributions.
1. Answer the following questions based on rolling a single six-sided die.
a) If you roll a single die and count the number of dots on top, what is the sample space of all possible outcomes? Are the outcomes equally likely?
b) Assign probabilities to the outcomes of the sample space of part (a). Do the probabilities add up to 1? Should they add up to 1? Explain.
c) What is the probability of getting a number less than 4 on a single throw?
d) What is the probability of getting a 3 or 4 on a single throw?
2. You draw two cards while playing Blackjack from a standard deck of 52 cards without replacing the first one before drawing the second.
3. You have three pancakes. One is golden on both sides, one is brown on both sides and one is golden on one side and brown on the other. You choose one pancake at random and see that one side is brown. Find the probability that the other side of the pancake is brown.
4. You wish to play a three-number lottery with your favorite data 8, 2 and 5. After a number is drawn, the number is placed back in the container for the next draw. What is the probability that the three winning numbers will be 8, 2 and 5? Are the numbers independent of each other? How would the probability change if no repetition is allowed?
5. Have you ever tried to get out of jury duty? About 25% of those called will find an excuse to avoid it. If 12 people are called for jury duty.
a) What is the probability that all 12 will be available to serve on the jury?
b) What is the probability that 6 or more will not be available to serve on the jury?
c) Find the expected number of those available to serve on the jury.
