Learning Objectives<\/h3>\r\nCounting Principles\r\n\r\n \t- Solve counting problems using the Addition Principle and the\u00a0Multiplication Principle.<\/span><\/li>\r\n \t
- Solve counting problems using permutations and combinations \u00a0involving n distinct objects.<\/span><\/li>\r\n \t
- Find the number of subsets of a given set.<\/span><\/li>\r\n \t
- Solve counting problems using permutations involving n non-distinct objects.<\/span><\/li>\r\n \t
- Apply the Binomial Theorem<\/span><\/li>\r\n<\/ul>\r\n
Probability<\/span><\/p>\r\n\r\n\r\n \t- Construct probability models.<\/span><\/li>\r\n \t
- Compute probabilities of equally likely outcomes.<\/span><\/li>\r\n \t
- Compute probabilities of the union of two events.<\/span><\/li>\r\n \t
- Use the complement rule to find probabilities.<\/span><\/li>\r\n \t
- Compute probability using counting theory.<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n ","rendered":"
According to the news, the lottery jackpot is climbing by the hour. \u00a0Long lines of dreamers are forming wherever lottery tickets are sold. \u00a0While you don\u2019t usually buy lottery tickets, it is getting tempting. \u00a0Just imagine what you could do with $100 million dollars. \u00a0Perhaps you could retire early or never even go to work. \u00a0Maybe visit a beautiful island. \u00a0All you need to do is pick the correct numbers, and the jackpot is all yours.<\/p>\n
![\"Image](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/03\/22214133\/lotto-864035_1920-300x298.jpg\")
<\/p>\n
<\/p>\n
It sounds easy enough; just six simple numbers. \u00a0But how likely are you to win? \u00a0And could you increase the likelihood of winning by purchasing more lottery tickets?<\/p>\n
<\/p>\n
To answer these questions, you need to know about permutations and combinations. \u00a0So learn about them as you complete this module, and then we\u2019ll return to the lottery at the end. \u00a0Then you\u2019ll be able to decide whether you want to stand in line to purchase a ticket.<\/p>\n
![\"Photo](\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/896\/2017\/03\/22214638\/sea-418742_1920-300x225.jpg\")
<\/p>\n
<\/p>\n
\nLearning Objectives<\/h3>\n
Counting Principles<\/p>\n
\n- Solve counting problems using the Addition Principle and the\u00a0Multiplication Principle.<\/span><\/li>\n
- Solve counting problems using permutations and combinations \u00a0involving n distinct objects.<\/span><\/li>\n
- Find the number of subsets of a given set.<\/span><\/li>\n
- Solve counting problems using permutations involving n non-distinct objects.<\/span><\/li>\n
- Apply the Binomial Theorem<\/span><\/li>\n<\/ul>\n
Probability<\/span><\/p>\n\n- Construct probability models.<\/span><\/li>\n
- Compute probabilities of equally likely outcomes.<\/span><\/li>\n
- Compute probabilities of the union of two events.<\/span><\/li>\n
- Use the complement rule to find probabilities.<\/span><\/li>\n
- Compute probability using counting theory.<\/span><\/li>\n<\/ul>\n<\/div>\n
<\/p>\n\n\t\t\t \n\t\t\t Candela Citations<\/h3>\n\t\t\t\t\t \n\t\t\t\t\t\t \n\t\t\t\t\t\t\t CC licensed content, Original<\/div>- Why It Matters: Probability and Counting Principles. Authored by<\/strong>: Lumen Learning. License<\/strong>: CC BY: Attribution<\/a><\/em><\/li><\/ul>CC licensed content, Shared previously<\/div>
- Numbered balls for lottery. Located at<\/strong>: https:\/\/pixabay.com\/en\/lotto-balls-gambling-lottery-864035\/<\/a>. License<\/strong>: CC0: No Rights Reserved<\/a><\/em><\/li>
- Beach bay. Located at<\/strong>: https:\/\/pixabay.com\/en\/sea-bay-waterfront-beach-nice-418742\/<\/a>. License<\/strong>: CC0: No Rights Reserved<\/a><\/em><\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17533,"menu_order":1,"template":"","meta":{"_candela_citation":"[{\"type\":\"original\",\"description\":\"Why It Matters: Probability and Counting Principles\",\"author\":\"Lumen Learning\",\"organization\":\"\",\"url\":\"\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Numbered balls for lottery\",\"author\":\"\",\"organization\":\"\",\"url\":\"https:\/\/pixabay.com\/en\/lotto-balls-gambling-lottery-864035\/\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"},{\"type\":\"cc\",\"description\":\"Beach bay\",\"author\":\"\",\"organization\":\"\",\"url\":\"https:\/\/pixabay.com\/en\/sea-bay-waterfront-beach-nice-418742\/\",\"project\":\"\",\"license\":\"cc0\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"3c94fb2b-2db1-4da8-bb48-c23b3b91c151","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3825","chapter","type-chapter","status-publish","hentry"],"part":2518,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/3825","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/users\/17533"}],"version-history":[{"count":7,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/3825\/revisions"}],"predecessor-version":[{"id":3923,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/3825\/revisions\/3923"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/parts\/2518"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapters\/3825\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/media?parent=3825"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/pressbooks\/v2\/chapter-type?post=3825"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/contributor?post=3825"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/ivytech-wmopen-collegealgebra\/wp-json\/wp\/v2\/license?post=3825"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
Probability<\/span><\/p>\r\n\r\n According to the news, the lottery jackpot is climbing by the hour. \u00a0Long lines of dreamers are forming wherever lottery tickets are sold. \u00a0While you don\u2019t usually buy lottery tickets, it is getting tempting. \u00a0Just imagine what you could do with $100 million dollars. \u00a0Perhaps you could retire early or never even go to work. \u00a0Maybe visit a beautiful island. \u00a0All you need to do is pick the correct numbers, and the jackpot is all yours.<\/p>\n <\/p>\n It sounds easy enough; just six simple numbers. \u00a0But how likely are you to win? \u00a0And could you increase the likelihood of winning by purchasing more lottery tickets?<\/p>\n <\/p>\n To answer these questions, you need to know about permutations and combinations. \u00a0So learn about them as you complete this module, and then we\u2019ll return to the lottery at the end. \u00a0Then you\u2019ll be able to decide whether you want to stand in line to purchase a ticket.<\/p>\n <\/p>\n Counting Principles<\/p>\n Probability<\/span><\/p>\n <\/p>\n\n\t\t\t \r\n \t
<\/p>\n<\/p>\nLearning Objectives<\/h3>\n
\n
\n
Candela Citations<\/h3>\n\t\t\t\t\t