{"id":25946,"date":"2025-06-19T08:23:48","date_gmt":"2025-06-19T08:23:48","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=25946"},"modified":"2025-06-19T08:23:51","modified_gmt":"2025-06-19T08:23:51","slug":"a-contractor-is-considering-a-sale-that-promises-a-profit-of3000-with-a-probability-of-0-3","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/a-contractor-is-considering-a-sale-that-promises-a-profit-of3000-with-a-probability-of-0-3\/","title":{"rendered":"A contractor is considering a sale that promises a profit of3000 with a probability of 0.3."},"content":{"rendered":"\n
5) A contractor is considering a sale that promises a profit of 3000 with a probability of 0.3. What is the expected profit? A) 23,800 C) 21,700 16) (5 pts) If X is a hypergeometric random variable, compute P(X=3) for N = 8, K = 3, and n = 5. A) 0.714 B) 0.18 C) 0.179 D) Other: List the sample space and tell whether the events are equally likely. 17) Toss a fair coin five times; record the number of heads. A) {0, 1, 2, 3, 4, 5}, equally likely B) {1, 2, 3, 4, 5}, not equally likely C) {0, 1, 2, 3, 4, 5}, not equally likely D) {1, 2, 3, 4, 5}, equally likely E) {H, T}, equally likely<\/p>\n\n\n\n
The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n
Problem:<\/strong> A contractor is considering a sale that promises a profit of 3000 with a probability of 0.3. What is the expected profit?<\/p>\n\n\n\n
Answer:<\/strong> To calculate the expected profit, we use the formula for expected value<\/strong>:E=(Profit)\u00d7(Probability)+(0)\u00d7(1\u2212Probability)E = (Profit) \\times (Probability) + (0) \\times (1 – Probability)E=(Profit)\u00d7(Probability)+(0)\u00d7(1\u2212Probability)E=3000\u00d70.3+0\u00d70.7=900E = 3000 \\times 0.3 + 0 \\times 0.7 = 900E=3000\u00d70.3+0\u00d70.7=900<\/p>\n\n\n\n
Correct answer: $900<\/strong> (None of the answer choices listed match this. Possibly an error in options.)<\/p>\n\n\n\n
Explanation:<\/strong> Expected value gives the average profit the contractor can expect over many similar situations. In this case, there is only a 30 percent chance of gaining $3000 and a 70 percent chance of gaining nothing. Multiplying the profit by its probability gives an expected value of $900. This is a theoretical average; the contractor either earns $3000 or nothing in a single trial, but over many trials, the average would trend toward $900.<\/p>\n\n\n\n\n\n\n\n
K=3K = 3K=3: number of successes in the population<\/li>\n\n\n\n
n=5n = 5n=5: number of draws<\/li>\n\n\n\n
Find P(X=3)P(X = 3)P(X=3)<\/li>\n<\/ul>\n\n\n\n
Use the hypergeometric probability formula:P(X=k)=(Kk)(N\u2212Kn\u2212k)(Nn)P(X = k) = \\frac{{\\binom{K}{k} \\binom{N – K}{n – k}}}{{\\binom{N}{n}}}P(X=k)=(nN\u200b)(kK\u200b)(n\u2212kN\u2212K\u200b)\u200bP(X=3)=(33)(52)(85)=1\u00d71056=1056\u22480.179P(X = 3) = \\frac{{\\binom{3}{3} \\binom{5}{2}}}{{\\binom{8}{5}}} = \\frac{{1 \\times 10}}{{56}} = \\frac{10}{56} \\approx 0.179P(X=3)=(58\u200b)(33\u200b)(25\u200b)\u200b=561\u00d710\u200b=5610\u200b\u22480.179<\/p>\n\n\n\n
Correct answer: C) 0.179<\/strong><\/p>\n\n\n\n
Explanation:<\/strong> This problem models sampling without replacement<\/strong>, which is exactly what the hypergeometric distribution describes. We want the probability of drawing 3 “successes” (items of interest) when we randomly pick 5 items out of a population of 8 that contains 3 successes. Calculating the combinations involved allows us to find the probability accurately.<\/p>\n\n\n\n\n\n\n\n
Question 17: Sample Space for Coin Toss<\/strong><\/h3>\n\n\n\n
Situation:<\/strong> Toss a fair coin five times; record the number of heads.<\/p>\n\n\n\n
Sample space: {0, 1, 2, 3, 4, 5}<\/p>\n\n\n\n
Correct answer: C) {0, 1, 2, 3, 4, 5}, not equally likely<\/strong><\/p>\n\n\n\n
Explanation:<\/strong> Each individual outcome (like HHTHT) is equally likely, but the number<\/strong> of heads is not equally distributed. For example, there is only 1<\/strong> way to get all 5 heads, but there are 10<\/strong> different ways to get exactly 2 heads. Therefore, the possible numbers of heads range from 0 to 5, but each is not equally likely<\/strong> because some counts of heads occur in more outcome combinations than others.<\/p>\n\n\n\n\n\n\n\n
Summary of Correct Answers:<\/strong><\/h3>\n\n\n\n
Q17:<\/strong> C) {0, 1, 2, 3, 4, 5}, not equally likely<\/strong><\/li>\n<\/ul>\n\n\n\n<\/figure>\n","protected":false},"excerpt":{"rendered":"
5) A contractor is considering a sale that promises a profit of3000 with a probability of 0.3. What is the expected profit? A)23,800 C)21,700 16) (5 pts) If X is a hypergeometric random variable, compute P(X=3) for N = 8, K = 3, and n = 5. A) 0.714 B) 0.18 C) 0.179 D) Other: […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-25946","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25946","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=25946"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25946\/revisions"}],"predecessor-version":[{"id":25948,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/25946\/revisions\/25948"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=25946"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=25946"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=25946"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
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