Special Topics

Name ______Period ______Special Topics Homework Section 8.3 Day 1

1. A party host gives a door prize to one guest chosen at random. There are 42 men and 48 women at the party. What is the probability that the prize goes to a woman?

2. Abby, Boaz, Carmen, Dani, and Eduardo work in a firm's public relations office. Their employer must choose two of them to attend a conference in Paris. To avoid unfairness, the choice will be made by drawing two names from a hat. (This is an SRS of size 2.)

1. Write down all possible choices of two of the five names. This is the sample space.

2. The random drawing makes all choices equally likely. What is the probability of each choice?

3. What is the probability that Abby is chosen?

4. What is the probability that neither of the two men (Boaz and Eduardo) is chosen?

3. You toss a balanced coin 10 times and write down the resulting sequence of heads and tails, such as HTTTHHTHHH.

1. How many possible outcomes are there for the 10 tosses?

2. What is the probability that your 10-toss sequence is either all heads or all tails?

4. In the Texas Hold ‘Em style of poker, play begins with each player being dealt two cards face down. From a standard 52-card deck, how many possible 2-card hands could be dealt to you?

5. A computer assigns three-character log-in IDs that may contain the digits 0 to 9 as well as the letters a to z, with repeats allowed.

1. What is the probability that your ID contains no x?

2. What is the probability that your ID contains no digits? 6. Consider a typical “combination lock” on a locker or briefcase.

1. If you ask for the three numbers in the combination needed to open the lock, and they are given to you in numerical order as 3–5–8, why is this not enough information to open the lock?

2. What would be the probability that you could open the lock with one try?

3. Is such a lock accurately named or is it really a “permutation lock”?

7. You may have heard that a monkey hitting keys at random on a typewriter keyboard for an infinite amount of time could eventually type a particular chosen text, such as the complete works of Shakespeare. Let's focus on a monkey who just types the letters a, p, and s in random order. 1. How many possible three-letter “words” can the monkey type using only these letters?

2. Which of these are words in an English dictionary?

3. What is the probability that the word the monkey typed is in an English dictionary?

8. Mozart composed a 16-bar Viennese minuet (“Musical Dice Game”) in which bars #1–7 each have 11 choices, bar #8 has 2, bars #9–15 each have 11 and bar #16 has 1. How many possible versions of this minuet are there?

9. In poker, a royal flush is a 5-card hand containing (in any order) an Ace, King, Queen, Jack and 10 all of the same suit.

1. How many royal flush hands are possible?

2. What is the number of 5-card hands possible from a 52-card deck?

3. What is the probability that 5 cards drawn at random from a 52-card deck yield a royal flush?

10. Biblical Permutations: The King James Version Old Testament has its 39 books canonized in a different order than the Hebrew Bible does. What mathematical expression would yield the number of possible orders of these 39 books? Is this number larger than you expected?