{"id":2128,"date":"2015-11-12T18:30:41","date_gmt":"2015-11-12T18:30:41","guid":{"rendered":"https:\/\/courses.candelalearning.com\/collegealgebra1xmaster\/?post_type=chapter&p=2128"},"modified":"2017-04-03T20:36:35","modified_gmt":"2017-04-03T20:36:35","slug":"solutions-9","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/ivytech-collegealgebra\/chapter\/solutions-9\/","title":{"raw":"Solutions","rendered":"Solutions"},"content":{"raw":"

Solutions to Try Its<\/h2>\r\n1.\r\n\r\n\r\n\r\n\r\n\r\n\r\n
Outcome<\/th>\r\nProbability<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
Heads (H)<\/td>\r\n[latex]\\frac{1}{2}[\/latex]<\/td>\r\n<\/tr>\r\n
Tails (T)<\/td>\r\n[latex]\\frac{1}{2}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n\r\n2.\u00a0[latex]\\frac{2}{3}[\/latex]\r\n\r\n3.\u00a0[latex]\\frac{7}{13}[\/latex]\r\n\r\n4.\u00a0[latex]\\frac{2}{13}[\/latex]\r\n\r\n5.\u00a0[latex]\\frac{5}{6}[\/latex]\r\n\r\n6.\u00a0[latex]\\begin{array}{lll}\\text{a}\\text{. }\\frac{1}{91};\\hfill & \\text{b}\\text{. }\\frac{\\text{5}}{\\text{91}};\\hfill & \\text{c}\\text{. }\\frac{86}{91}\\hfill \\end{array}[\/latex]\r\n

Solutions to Odd-Numbered Exercises<\/h2>\r\n1.\u00a0probability; The probability of an event is restricted to values between [latex]0[\/latex] and [latex]1[\/latex], inclusive of [latex]0[\/latex] and [latex]1[\/latex].\r\n\r\n3.\u00a0An experiment is an activity with an observable result.\r\n\r\n5.\u00a0The probability of the union of two events<\/em> occurring is a number that describes the likelihood that at least one of the events from a probability model occurs. In both a union of sets [latex]A\\text{ } \\text{and }B[\/latex] and a union of events [latex]A \\text{and} B[\/latex], the union includes either [latex]A \\text{or} B[\/latex] or both. The difference is that a union of sets results in another set, while the union of events is a probability, so it is always a numerical value between [latex]0[\/latex] and [latex]1[\/latex].\r\n\r\n7.\u00a0[latex]\\frac{1}{2}[\/latex]\r\n\r\n9.\u00a0[latex]\\frac{5}{8}[\/latex]\r\n\r\n11.\u00a0[latex]\\frac{1}{2}[\/latex]\r\n\r\n13.\u00a0[latex]\\frac{3}{8}[\/latex]\r\n\r\n15.\u00a0[latex]\\frac{1}{4}[\/latex]\r\n\r\n17.\u00a0[latex]\\frac{3}{4}[\/latex]\r\n\r\n19.\u00a0[latex]\\frac{3}{8}[\/latex]\r\n\r\n21.\u00a0[latex]\\frac{1}{8}[\/latex]\r\n\r\n23.\u00a0[latex]\\frac{15}{16}[\/latex]\r\n\r\n25.\u00a0[latex]\\frac{5}{8}[\/latex]\r\n\r\n27.\u00a0[latex]\\frac{1}{13}[\/latex]\r\n\r\n29.\u00a0[latex]\\frac{1}{26}[\/latex]\r\n\r\n31.\u00a0[latex]\\frac{12}{13}[\/latex]\r\n\r\n33.\r\n\r\n \r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n\r\n
<\/th>\r\n1<\/th>\r\n2<\/th>\r\n3<\/th>\r\n4<\/th>\r\n5<\/th>\r\n6<\/th>\r\n<\/tr>\r\n<\/thead>\r\n
1<\/strong><\/td>\r\n(1, 1)\r\n2<\/td>\r\n(1, 2)\r\n3<\/td>\r\n(1, 3)\r\n4<\/td>\r\n(1, 4)\r\n5<\/td>\r\n(1, 5)\r\n6<\/td>\r\n(1, 6)\r\n7<\/td>\r\n<\/tr>\r\n
2<\/strong><\/td>\r\n(2, 1)\r\n3<\/td>\r\n(2, 2)\r\n4<\/td>\r\n(2, 3)\r\n5<\/td>\r\n(2, 4)\r\n6<\/td>\r\n(2, 5)\r\n7<\/td>\r\n(2, 6)\r\n8<\/td>\r\n<\/tr>\r\n
3<\/strong><\/td>\r\n(3, 1)\r\n4<\/td>\r\n(3, 2)\r\n5<\/td>\r\n(3, 3)\r\n6<\/td>\r\n(3, 4)\r\n7<\/td>\r\n(3, 5)\r\n8<\/td>\r\n(3, 6)\r\n9<\/td>\r\n<\/tr>\r\n
4<\/strong><\/td>\r\n(4, 1)\r\n5<\/td>\r\n(4, 2)\r\n6<\/td>\r\n(4, 3)\r\n7<\/td>\r\n(4, 4)\r\n8<\/td>\r\n(4, 5)\r\n9<\/td>\r\n(4, 6)\r\n10<\/td>\r\n<\/tr>\r\n
5<\/strong><\/td>\r\n(5, 1)\r\n6<\/td>\r\n(5, 2)\r\n7<\/td>\r\n(5, 3)\r\n8<\/td>\r\n(5, 4)\r\n9<\/td>\r\n(5, 5)\r\n10<\/td>\r\n(5, 6)\r\n11<\/td>\r\n<\/tr>\r\n
6<\/strong><\/td>\r\n(6, 1)\r\n7<\/td>\r\n(6, 2)\r\n8<\/td>\r\n(6, 3)\r\n9<\/td>\r\n(6, 4)\r\n10<\/td>\r\n(6, 5)\r\n11<\/td>\r\n(6, 6)\r\n12<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n35.\u00a0[latex]\\frac{5}{12}[\/latex]\r\n\r\n37.\u00a0[latex]0[\/latex]\r\n\r\n39.\u00a0[latex]\\frac{4}{9}[\/latex]\r\n\r\n41.\u00a0[latex]\\frac{1}{4}[\/latex]\r\n\r\n43.\u00a0[latex]\\frac{3}{4}[\/latex]\r\n\r\n45.\u00a0[latex]\\frac{21}{26}[\/latex]\r\n\r\n47.\u00a0[latex]\\frac{C\\left(12,5\\right)}{C\\left(48,5\\right)}=\\frac{1}{2162}[\/latex]\r\n\r\n49.\u00a0[latex]\\frac{C\\left(12,3\\right)C\\left(36,2\\right)}{C\\left(48,5\\right)}=\\frac{175}{2162}[\/latex]\r\n\r\n51.\u00a0[latex]\\frac{C\\left(20,3\\right)C\\left(60,17\\right)}{C\\left(80,20\\right)}\\approx 12.49%[\/latex]\r\n\r\n53.\u00a0[latex]\\frac{C\\left(20,5\\right)C\\left(60,15\\right)}{C\\left(80,20\\right)}\\approx 23.33%[\/latex]\r\n\r\n55.\u00a0[latex]20.50+23.33 - 12.49=31.34%[\/latex]\r\n\r\n57.\u00a0[latex]\\frac{C\\left(40000000,1\\right)C\\left(277000000,4\\right)}{C\\left(317000000,5\\right)}=36.78%[\/latex]\r\n\r\n59.\u00a0[latex]\\frac{C\\left(40000000,4\\right)C\\left(277000000,1\\right)}{C\\left(317000000,5\\right)}=0.11%[\/latex]","rendered":"

Solutions to Try Its<\/h2>\n

1.<\/p>\n\n\n\n\n\n\n
Outcome<\/th>\nProbability<\/th>\n<\/tr>\n<\/thead>\n
Heads (H)<\/td>\n[latex]\\frac{1}{2}[\/latex]<\/td>\n<\/tr>\n
Tails (T)<\/td>\n[latex]\\frac{1}{2}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

2.\u00a0[latex]\\frac{2}{3}[\/latex]<\/p>\n

3.\u00a0[latex]\\frac{7}{13}[\/latex]<\/p>\n

4.\u00a0[latex]\\frac{2}{13}[\/latex]<\/p>\n

5.\u00a0[latex]\\frac{5}{6}[\/latex]<\/p>\n

6.\u00a0[latex]\\begin{array}{lll}\\text{a}\\text{. }\\frac{1}{91};\\hfill & \\text{b}\\text{. }\\frac{\\text{5}}{\\text{91}};\\hfill & \\text{c}\\text{. }\\frac{86}{91}\\hfill \\end{array}[\/latex]<\/p>\n

Solutions to Odd-Numbered Exercises<\/h2>\n

1.\u00a0probability; The probability of an event is restricted to values between [latex]0[\/latex] and [latex]1[\/latex], inclusive of [latex]0[\/latex] and [latex]1[\/latex].<\/p>\n

3.\u00a0An experiment is an activity with an observable result.<\/p>\n

5.\u00a0The probability of the union of two events<\/em> occurring is a number that describes the likelihood that at least one of the events from a probability model occurs. In both a union of sets [latex]A\\text{ } \\text{and }B[\/latex] and a union of events [latex]A \\text{and} B[\/latex], the union includes either [latex]A \\text{or} B[\/latex] or both. The difference is that a union of sets results in another set, while the union of events is a probability, so it is always a numerical value between [latex]0[\/latex] and [latex]1[\/latex].<\/p>\n

7.\u00a0[latex]\\frac{1}{2}[\/latex]<\/p>\n

9.\u00a0[latex]\\frac{5}{8}[\/latex]<\/p>\n

11.\u00a0[latex]\\frac{1}{2}[\/latex]<\/p>\n

13.\u00a0[latex]\\frac{3}{8}[\/latex]<\/p>\n

15.\u00a0[latex]\\frac{1}{4}[\/latex]<\/p>\n

17.\u00a0[latex]\\frac{3}{4}[\/latex]<\/p>\n

19.\u00a0[latex]\\frac{3}{8}[\/latex]<\/p>\n

21.\u00a0[latex]\\frac{1}{8}[\/latex]<\/p>\n

23.\u00a0[latex]\\frac{15}{16}[\/latex]<\/p>\n

25.\u00a0[latex]\\frac{5}{8}[\/latex]<\/p>\n

27.\u00a0[latex]\\frac{1}{13}[\/latex]<\/p>\n

29.\u00a0[latex]\\frac{1}{26}[\/latex]<\/p>\n

31.\u00a0[latex]\\frac{12}{13}[\/latex]<\/p>\n

33.<\/p>\n

 <\/p>\n\n\n\n\n\n\n\n\n\n\n
<\/th>\n1<\/th>\n2<\/th>\n3<\/th>\n4<\/th>\n5<\/th>\n6<\/th>\n<\/tr>\n<\/thead>\n
1<\/strong><\/td>\n(1, 1)
\n2<\/td>\n		(1, 2)
\n3<\/td>\n		(1, 3)
\n4<\/td>\n		(1, 4)
\n5<\/td>\n		(1, 5)
\n6<\/td>\n		(1, 6)
\n7<\/td>\n<\/tr>\n
2<\/strong><\/td>\n(2, 1)
\n3<\/td>\n		(2, 2)
\n4<\/td>\n		(2, 3)
\n5<\/td>\n		(2, 4)
\n6<\/td>\n		(2, 5)
\n7<\/td>\n		(2, 6)
\n8<\/td>\n<\/tr>\n
3<\/strong><\/td>\n(3, 1)
\n4<\/td>\n		(3, 2)
\n5<\/td>\n		(3, 3)
\n6<\/td>\n		(3, 4)
\n7<\/td>\n		(3, 5)
\n8<\/td>\n		(3, 6)
\n9<\/td>\n<\/tr>\n
4<\/strong><\/td>\n(4, 1)
\n5<\/td>\n		(4, 2)
\n6<\/td>\n		(4, 3)
\n7<\/td>\n		(4, 4)
\n8<\/td>\n		(4, 5)
\n9<\/td>\n		(4, 6)
\n10<\/td>\n<\/tr>\n
5<\/strong><\/td>\n(5, 1)
\n6<\/td>\n		(5, 2)
\n7<\/td>\n		(5, 3)
\n8<\/td>\n		(5, 4)
\n9<\/td>\n		(5, 5)
\n10<\/td>\n		(5, 6)
\n11<\/td>\n<\/tr>\n
6<\/strong><\/td>\n(6, 1)
\n7<\/td>\n		(6, 2)
\n8<\/td>\n		(6, 3)
\n9<\/td>\n		(6, 4)
\n10<\/td>\n		(6, 5)
\n11<\/td>\n		(6, 6)
\n12<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

35.\u00a0[latex]\\frac{5}{12}[\/latex]<\/p>\n

37.\u00a0[latex]0[\/latex]<\/p>\n

39.\u00a0[latex]\\frac{4}{9}[\/latex]<\/p>\n

41.\u00a0[latex]\\frac{1}{4}[\/latex]<\/p>\n

43.\u00a0[latex]\\frac{3}{4}[\/latex]<\/p>\n

45.\u00a0[latex]\\frac{21}{26}[\/latex]<\/p>\n

47.\u00a0[latex]\\frac{C\\left(12,5\\right)}{C\\left(48,5\\right)}=\\frac{1}{2162}[\/latex]<\/p>\n

49.\u00a0[latex]\\frac{C\\left(12,3\\right)C\\left(36,2\\right)}{C\\left(48,5\\right)}=\\frac{175}{2162}[\/latex]<\/p>\n

51.\u00a0[latex]\\frac{C\\left(20,3\\right)C\\left(60,17\\right)}{C\\left(80,20\\right)}\\approx 12.49%[\/latex]<\/p>\n

53.\u00a0[latex]\\frac{C\\left(20,5\\right)C\\left(60,15\\right)}{C\\left(80,20\\right)}\\approx 23.33%[\/latex]<\/p>\n

55.\u00a0[latex]20.50+23.33 - 12.49=31.34%[\/latex]<\/p>\n

57.\u00a0[latex]\\frac{C\\left(40000000,1\\right)C\\left(277000000,4\\right)}{C\\left(317000000,5\\right)}=36.78%[\/latex]<\/p>\n

59.\u00a0[latex]\\frac{C\\left(40000000,4\\right)C\\left(277000000,1\\right)}{C\\left(317000000,5\\right)}=0.11%[\/latex]<\/p>\n\n\t\t\t

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