{"id":54648,"date":"2021-09-30T08:59:43","date_gmt":"2021-09-30T08:59:43","guid":{"rendered":"https:\/\/papersspot.com\/blog\/2021\/09\/30\/probability-one-question\/"},"modified":"2021-09-30T08:59:43","modified_gmt":"2021-09-30T08:59:43","slug":"probability-one-question","status":"publish","type":"post","link":"https:\/\/papersspot.com\/blog\/2021\/09\/30\/probability-one-question\/","title":{"rendered":"Probability (One Question)"},"content":{"rendered":"<p>Pooh\u2019s Home Run Derby is a flash game supposedly made for children but notorious for its<br \/> extreme difficulty. The objective of each level is simply to score a certain amount of home runs within a<br \/> limited number of pitches. In the final level, you face Christopher Robin and must score at least 40 home<br \/> runs in 50 pitches. Suppose that through hours of practice, you are able to score a home run on one of<br \/> Christopher\u2019s pitches with probability of 0.7. Assume each pitch is independent. Calculate: <br \/>(a) The probability of winning in exactly 40 rounds <br \/>(b) The probability of winning in exactly 41 rounds <br \/>(c) The probability of winning in exactly 42 rounds <br \/>(d) The probability of winning (hint: generalize the previous results and express your answer as a<br \/> summation)<br \/> Let X be a random variable for the total number of pitches it takes to win (for the purpose of simplicity,<br \/> X may still map to a positive value greater than 50). Let W be a binary random variable returning 1 when<br \/> we win and 0 when we lose (in a 50 pitch game). Please frame your answers in terms of these variables<br \/> when applicable. <\/p>\n","protected":false},"excerpt":{"rendered":"<p>Pooh\u2019s Home Run Derby is a flash game supposedly made for children but notorious for its extreme difficulty. The objective of each level is simply to score a certain amount of home runs within a limited number of pitches. In the final level, you face Christopher Robin and must score at least 40 home runs [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[10],"class_list":["post-54648","post","type-post","status-publish","format-standard","hentry","category-research-paper-writing","tag-writing"],"_links":{"self":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/54648","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/comments?post=54648"}],"version-history":[{"count":0,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/posts\/54648\/revisions"}],"wp:attachment":[{"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/media?parent=54648"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/categories?post=54648"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/papersspot.com\/blog\/wp-json\/wp\/v2\/tags?post=54648"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}