{"id":23254,"date":"2022-01-06T07:02:07","date_gmt":"2022-01-06T07:02:07","guid":{"rendered":"https:\/\/assignmenttutors.net\/blog\/5-4-in-the-carnival-game-under-or-over-seven-a-pair-of-fair-dice-is\/"},"modified":"2022-01-06T07:02:07","modified_gmt":"2022-01-06T07:02:07","slug":"5-4-in-the-carnival-game-under-or-over-seven-a-pair-of-fair-dice-is","status":"publish","type":"post","link":"https:\/\/assignmenttutors.net\/blog\/5-4-in-the-carnival-game-under-or-over-seven-a-pair-of-fair-dice-is\/","title":{"rendered":"5.4 in the carnival game under-or-over-seven, a pair of fair dice is"},"content":{"rendered":"
\n

5.4 In the carnival game Under-or-Over-Seven, a pair of fair<\/p>\n

dice is rolled once, and the resulting sum determines whether<\/p>\n

the player wins or loses his or her bet. For example, the player<\/p>\n

can bet $1 that the sum will be under 7-that is, 2, 3, 4, 5, or<\/p>\n

6. For this bet, the player wins $1 if the result is under 7 and<\/p>\n

loses $1 if the outcome equals or is greater than 7. Similarly,<\/p>\n

the player can bet $1 that the sum will be over 7-that is, 8, 9,<\/p>\n

10, II, or 12. Here, the player wins $1 if the result is over 7<\/p>\n

but loses $1 if the result is 7 or under. A third method of play<\/p>\n

is to bet $1 on the outcome 7. For this bet, the player wins $4<\/p>\n

if the result of the roll is 7 and loses $1 otherwise.<\/p>\n

a. Construct the probability distribution representing the<\/p>\n

different outcomes that are possible for a $1 bet on<\/p>\n

under 7.<\/p>\n

b. Construct the probability distribution representing the different<\/p>\n

outcomes that are possible for a $] bet on over 7.<\/p>\n

c. Construct the probability distribution representing the<\/p>\n

different outcomes that are possible for a $1 bet on 7,<\/p>\n

d. Show that the expected long-run profit (or loss) to the<\/p>\n

player is the same, no matter which method of play is used.<\/p>\n

\u00a0<\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

5.4 In the carnival game Under-or-Over-Seven, a pair of fair dice is rolled once, and the resulting sum determines whether the player wins or loses his or her bet. For example, the player can bet $1 that the sum will be under 7-that is, 2, 3, 4, 5, or 6. For this bet, the player […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[16],"tags":[],"class_list":["post-23254","post","type-post","status-publish","format-standard","hentry","category-education"],"_links":{"self":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/23254","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/comments?post=23254"}],"version-history":[{"count":0,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/posts\/23254\/revisions"}],"wp:attachment":[{"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/media?parent=23254"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/categories?post=23254"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/assignmenttutors.net\/blog\/wp-json\/wp\/v2\/tags?post=23254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}