{"id":8013,"date":"2011-08-24T06:00:23","date_gmt":"2011-08-24T13:00:23","guid":{"rendered":"https:\/\/gmatclub.com\/blog\/?p=8013"},"modified":"2011-07-20T15:19:05","modified_gmt":"2011-07-20T22:19:05","slug":"kaplan-gmat-sample-problem-probability-problem-solving","status":"publish","type":"post","link":"https:\/\/gmatclub.com\/blog\/kaplan-gmat-sample-problem-probability-problem-solving\/","title":{"rendered":"Kaplan GMAT Sample Problem: Probability Problem Solving"},"content":{"rendered":"

\"\"<\/a> Try this advanced GMAT<\/a> probability question, testing your knowledge of the ins and outs of how probability works. <\/p>\n

Problem:<\/strong>
\nThe events A and B are independent. The probability that event A occurs is 0.6, and the probability that at least one of the events A and B occurs is 0.94. What is the probability that event B occurs?
\n(A) 0.34
\n(B) 0.65
\n(C) 0.72
\n(D) 0.76
\n(E) 0.85<\/p>\n

Solution:<\/strong>
\nIn order to find the probability that event B occurs in this problem, we need to set up and equation that includes the probabilities we are given and allows us to solve for B. We are told that the probability that at least one of A or B occurring is 0.94. \u2018At least one of A or B\u2019 means that an outcome is desired if A occurs and B does not, B occurs and A does not or A and B both occur.<\/p>\n

It is important to remember two rules of probability here. First, when you encounter an \u2018or\u2019 situation you add and when you see an \u2018and\u2019 situation you multiply. Second, the probability that an event does NOT occur is equal to one minus the probability it does occur.<\/p>\n

Based on these rules, we can translate \u2018at least one of A or B occurs is 0.94\u2019 to the following equation:
\n.6B [the probability that both A and B occur] + .6(1-B) [the probability that A occurs and B does not] + B(1-.6) [the probability that B occurs and A does not] = .94<\/p>\n

We can simplify this equation to .6B + .6(1-B) + .4B = .94 and solve for B.
\n.6B + .6(1-B) + .4B = .94
\n.6B + .6 - .6B + .4B = .94
\n.6 + .4B = .94
\n.4B = .34
\nB = .34\/.4
\nB = 34\/40 = .85<\/p>\n

Thus, our answer is 0.85, or answer choice (E).<\/p>\n

~Bret Ruber<\/p>\n","protected":false},"excerpt":{"rendered":"

Try this advanced GMAT probability question, testing your knowledge of the ins and outs of how probability works. Problem: The events A and B are independent. The probability that event…<\/p>\n","protected":false},"author":120,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[9,558,243,717,736],"tags":[],"class_list":["post-8013","post","type-post","status-publish","format-standard","hentry","category-gmat","category-kaplan-blog","category-blog","category-problem-solving-gmat","category-quant-gmat","entry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/8013","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/users\/120"}],"replies":[{"embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/comments?post=8013"}],"version-history":[{"count":1,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/8013\/revisions"}],"predecessor-version":[{"id":8014,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/posts\/8013\/revisions\/8014"}],"wp:attachment":[{"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/media?parent=8013"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/categories?post=8013"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gmatclub.com\/blog\/wp-json\/wp\/v2\/tags?post=8013"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}