(1) Let's practice making new sets out of old sets! Say A = {chocolate, vanilla, strawberry} and B = {caramel, whipped cream} (a) What is A x B? (b) What is P(B)? (c) If the ice cream flavors are chocolate, vanilla, and strawberry, and the toppings are caramel and whipped cream, and you're allowed to have as many different flavors and toppings as you like, what would that set be?

(1) Let's practice making new sets out of old sets! Say A = {chocolate, vanilla, strawberry} and B = {caramel, whipped cream} (a) What is A x B? (b) What is P(B)? (c) If the ice cream flavors are chocolate, vanilla, and strawberry, and the toppings are caramel and whipped cream, and you're allowed to have as many different flavors and toppings as you like, what would that set be?

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section8.6: Counting Principles

Problem 74E: Lottery Powerball is a lottery game that is operated by the Multi-State Lottery Association and is...

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Lottery Powerball is a lottery game that is operated by the Multi-State Lottery Association and is played in 44 states, Washington D.C., Puerto Rico, and the U.S. Virgin Islands. The game is played by drawing five white balls out of a drum of 69 white balls (numbered 1-69) and one red powerball out of a drum of 26 red balls (numbered 1-26). The jackpot is won by matching all five white balls in any order and the red powerball. (a) Find the possible number of winning Powerball numbers. (b) Find the possible number of winning Powerball numbers when you win the jackpot by matching all five white balls in order and the red powerball.
2. The physicist Frank Benford noticed in the 1930s that, for many sets of numbers in the real world, the leading digit* of the number is more likely to be a small number than a larger one (i.e., 1’s and 2’s are more common than 8’s and 9’s). In fact, many wide-ranging number sets obey “Benford’s Law,” which says that 1’s are about 30.1% of the leading digits, 2’s are 17.6%, 3’s are 12.5%, 4’s are 9.7%, 5’s are 7.9%, 6’s are 6.7%, 7’s are 5.8%, 8’s are 5.1%, and 9’s are 4.6%. Benford’s Law has been used to identify accounting fraud and made-up scientific data. *leading digit is the first significant digit; e.g., “1” in the number 132, “2” in the number .0026.S uppose I suspect my research collaborator of faking a dataset that represents the price that people say is the average amount they pay each month in health care deductibles and copayments, rounded to the nearest dollar.10 50 15 11 412 80 48 13 4250 10 68 41 790 15 139 147 1433 61 145 7 406 99 50 27 7513 40 3 21 1475 203 148 27…
What is meant by Union of sets?
The five most common words appearing in spam emails are shipping!, today!, here!,available, and fingertips! (Andy Greenberg, “The Most Common Words In Spam Email,”Forbes website, March 17, 2010). Many spam filters separate spam from ham (email notconsidered to be spam) through application of bayes’ theorem. Suppose that for one emailaccount, 1 in every 10 messages is spam and the proportions of spam messages that havethe five most common words in spam email are given below.shipping! .051today! .045here! .034available .014fingertips! .014Also suppose that the proportions of ham messages that have these words areshipping! .0015today! .0022here! .0022available .0041fingertips! .0011a. If a message includes the word shipping!, what is the probability the message is spam?If a message includes the word shipping!, what is the probability the message is ham?Should messages that include the word shipping! be flagged as spam?b. If a message includes the word today!, what is the probability the…
The five most common words appearing in spam emails are shipping!, today!, here!,available, and fingertips! (Andy Greenberg, “The Most Common Words In Spam Email,”Forbes website, March 17, 2010). Many spam filters separate spam from ham (email notconsidered to be spam) through application of bayes’ theorem. Suppose that for one emailaccount, 1 in every 10 messages is spam and the proportions of spam messages that havethe five most common words in spam email are given below.shipping! .051today! .045here! .034available .014fingertips! .014Also suppose that the proportions of ham messages that have these words areshipping! .0015today! .0022here! .0022available .0041fingertips! .0011a. If a message includes the word shipping!, what is the probability the message is spam?If a message includes the word shipping!, what is the probability the message is ham?Should messages that include the word shipping! be flagged as spam?b. If a message includes the word today!, what is the probability the…
The five most common words appearing in spam emails are shipping!, today!, here!,available, and fingertips! (Andy Greenberg, “The Most Common Words In Spam Email,”Forbes website, March 17, 2010). Many spam filters separate spam from ham (email notconsidered to be spam) through application of bayes’ theorem. Suppose that for one emailaccount, 1 in every 10 messages is spam and the proportions of spam messages that havethe five most common words in spam email are given below.shipping! .051today! .045here! .034available .014fingertips! .014Also suppose that the proportions of ham messages that have these words areshipping! .0015today! .0022here! .0022available .0041fingertips! .0011a. If a message includes the word shipping!, what is the probability the message is spam?If a message includes the word shipping!, what is the probability the message is ham?Should messages that include the word shipping! be flagged as spam?
Bag A contains 10 balls of which 3 are red and 7 are blue(assume that each ball is numbered, so all balls are different from each other). Bag Y contains 10 balls of which 4 are red and 6 are blue(assume that each ball is numbered, so all balls are different from each other). In how many ways you could pick one red ball and one blue ball if one ball is picked from each of the bag?