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Problem 10

List the elements in the given set. The set of outcomes (a) of tossing three distinguishable coins and (b) of tossing three indistinguishable coins [HINT: See Example 1.]

Expert verified

(a) For three distinguishable coins, there are 8 possible outcomes: HHH, HHT, HTH, THH, HTT, TTH, THT, TTT.
(b) For three indistinguishable coins, there are 4 possible outcomes based on the number of Heads and Tails: 3H 0T (HHH), 2H 1T (e.g., HHT), 1H 2T (e.g., HTT), 0H 3T (TTT).

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Chapter 6

Popular Movies in 2011 Exercises 69 and 70 are based on the following list of top DVD rentals (based on revenue) for the weekend ending November 6,\(2011:^{26}\) $$ \begin{array}{|l|c|} \hline \text { Title } & \text { Rank } \\ \hline \text { Captain America: The First Avenger } & 1 \\ \hline \text { Bad Teacher } & 2 \\ \hline \text { Fast Five } & 3 \\ \hline \text { Cars 2 } & 4 \\ \hline \text { Trespass } & 5 \\ \hline \text { Bridesmaids } & 6 \\ \hline \text { Zookeeper } & 7 \\ \hline \text { Transformers: Dark of the Moon } & 8 \\ \hline \text { Scream } & 9 \\ \hline \text { Thor } & 10 \\ \hline \end{array} $$ Rather than studying for math, you and your buddies decide to get together for a marathon movie-watching, popcorn-guzzling event on Saturday night. You decide to watch four movies selected at random from the above list. a. How many sets of four movies are possible? b. Your best friends, the Lara twins, refuse to see Bridesmaids on the grounds that it is "for girlie men" and also insist that at least one of Captain America or Thor be among the movies selected. How many of the possible groups of four will satisfy the twins? c. Comparing the answers in parts (a) and (b), would you say that the Lara twins are more likely than not to be satisfied with your random selection?

Chapter 6

Databases A freelance computer consultant keeps a database of her clients, which contains the names \(S=\\{\) Acme, Brothers, Crafts, Dion, Effigy, Floyd, Global, Hilbert \(\\}\) The following clients owe her money: \(A=\\{\) Acme, Crafts, Effigy, Global \(\\}\) The following clients have done at least \(\$ 10,000\) worth of business with her: \(B=\\{\) Acme, Brothers, Crafts, Dion \(\\} .\) The following clients have employed her in the last year: \(C=\\{\) Acme, Crafts, Dion, Effigy, Global, Hilbert \(\\}\). In Exercises \(61-68,\) a subset of clients is described that the consultant could find using her database. Write the subset in terms of \(A, B,\) and \(C,\) and list the clients in that subset. [HINT: See Example \(4.]\) The clients who owe her money and have done at least \(\$ 10,000\) worth of business with her

Chapter 6

At the beginning of \(2002,\) Baskin-Robbins claimed to have "nearly 1,000 different ice cream flavors." 13 Assuming that you could choose from 1,000 different flavors, that you could have a single flavor of ice cream in a cone, a cup, or a sundae, and that you could choose from a dozen different toppings, how many different desserts could you have?

Chapter 6

You are searching online for techno music that is neither European nor Dutch. In set notation, which set of music files are you searching for? (A) Techno \(\cap\) (European \(\cap\) Dutch)' (B) Techno \(\cap\) (European \(\cup\) Dutch)' (C) Techno \(\cup\) (European \(\cap\) Dutch)' (D) Techno \(\cup\) (European \(\cup\) Dutch)'

Chapter 6

Here is a list of the main characters in Shakespeare's Romeo and Juliet. The first seven characters are male, and the last four are female. Escalus, prince of Verona Paris, kinsman to the prince Romeo, of Montague Household Mercutio, friend of Romeo Benvolio, friend of Romeo Tybalt, nephew to Lady Capulet Friar Lawrence, a Franciscan Lady Montague, of Montague Household Lady Capulet, of Capulet Household Juliet, of Capulet Household Juliet's Nurse A total of 10 male and 8 female actors are available to play these roles. How many possible casts are there? (All roles are to be played by actors of the same gender as the character.)

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