Q1-18 Section 8.1

Question 1 4 pts Given the following Venn diagram: Data A B 0.39 0.27 0.18 0.16 Note: When answering the questions below, for any final answer that has up to four decimal places, enter your answer without rounding the number. For any answers with more than four decimal values, round your final answer to four decimal places. a) Calculate the probability P (A| B) =? b) Calculate the probability P (B|A) =?Question 2 4 pts Given the following Venn diagram: DATA A B 0.3 0.26 0.29 0.15 Note: When answering the questions below, for any final answer that has up to four decimal places, enter your answer without rounding the number. For any answers with more than four decimal values, round your final answer to four decimal places. a) Calculate the probability P (A| B) =? b) Calculate the probability P (B| A) =?Given the following Venn diagram: Data A B 0.19 0.14 0.56 0.11 Note: When answering the questions below, for any final answer that has up to four decimal places, enter your answer without rounding the number. For any answers with more than four decimal values, round your final answer to four decimal places. a) Calculate the probability P (A| B) =? b) Calculate the probability P (B|A) =?Question 4 3 pts Suppose 9 orange and 3 blue identical objects are in ajar. A blindfolded person randomly selects two of these objects from the jar one after another, without replacing them back into the jar. The following tree diagram depicts all the possible random outcomes, but the branch probabilities are missing. [range C \"Orangezd ___,. Blue a 2:4], $Blue Y e \\'Orange f \\Blue Note: For all questions below, please enter your answers in fraction form. a) What is the value of the branch probability 1) =? b) What is the value of the branch probability 9 =? c) What is the value of the branch probability 6 =? Question 5 3 pts Suppose 6 green and 3 blue identical objects are in a jar. A blindfolded person randomly selects two of these objects from the jar one after another, without replacing them back into the jar. The following tree diagram depicts all the possible random outcomes, but the branch probabilities are missing. Green c/ a \"Greenzd '>Blue \"1 33 b '1\" Blue V 9 \"Green f \\Blue Note: For all questions below, please enter your answers in fraction form. a) What is the value of the branch probability a =? b) What is the value of the branch probability d =? c) What is the value of the branch probability 6 =? Question 6 3 pts Suppose 5 blue and 2 yellow identical objects are in a jar. A blindfolded person randomly selects two of these objects from the jar one after another, without replacing them back into the jar. The following tree diagram depicts all the possible random outcomes, but the branch probabilities are missing. *ellow Note: For all questions below, please enter your answers in fraction form. a) What is the value of the branch probability a =? b) What is the value of the branch probability 9 2? c) What is the value of the branch probability 6 =? Question 7 3 pts If E and F are events with P(En F) =0.089 , and P(E| F) =0.596 , find P (F) =? Note: For any final answer that has up to four decimal places, enter your answer in the box below without rounding the number. For any answer with more than four decimal values, round your final answer to four decimal places. Question 8 3 pts If E and F are events with P (E) =0.347 , P(F) =0.377 , and P(En F) = 0.092 , calculate P (E| F) =? Note: For any final answer that has up to four decimal places, enter your answer in the box below without rounding the number. For any answer with more than four decimal values, round your final answer to four decimal places.Question 9 3 pts If E and F are events with P (E) =0.412 , P(F) =0.412 , and P(En F) =0.2 , calculate P (F|E) =? Note: For any final answer that has up to four decimal places, enter your answer in the box below without rounding the number. For any answer with more than four decimal values, round your final answer to four decimal places. Question 10 3 pts Let E and F be the events in a sample space S for which P (E) =0.401 , P (F) = 0.554 , and P(E U F) =0.785 , calculate P (F|E) =? Note: For any final answer that has up to four decimal places, enter your answer in the box below without rounding the number. For any answer with more than four decimal values, round your final answer to four decimal places.Question 11 3 pts Let E and F be the events in a sample space S such that P(E|F) =0.348 , P(F) =0.451. Calculate P(E n F) =? Note: For any final answer that has up to four decimal places, enter your answer in the box below without rounding the number. For any answer with more than four decimal values, round your nal answer to four decimal places. Question 12 3 pts Suppose 8 red and 4 orange identical objects are in ajar.A blindfolded person randomly selects two of these objects from the jar one after another, without replacing them back into the jar. The following tree diagram depicts all the possible random outcomes and their probabilities. 7m R9\\ 4111 I \"Orange 3/12 a R 4 O 4112 range am \"Red 3m Orange Note: Please enter your answers below in fraction form. a) What is the conditional probability P (Red | Orange) =? b) What is the probability of obtaining a nal outcome with rst a red object and then an orange object? Question 13 3 pts Suppose 5 yellow and 2 blue identical objects are in a jar. A blindfolded person randomly selects two of these objects from the jar one after another, without replacing them back into the jar. The following tree diagram depicts all the possible random outcomes and their probabilities. Yellow 4/6 )eu 2,6 H) Blue 5/? \"K 23 2'7 '> Blue 5/6 \"Yellow Note: Please enter your answers below in fraction form. a) What is the conditional probability P (Yellow | Blue) =? b) What is the probability of obtaining a nal outcome with one blue object? Suppose 4 green and 5 red identical objects are in a jar. A blindfolded person randomly selects two of these objects from the jar one after another, without replacing them back into the jar. The following tree diagram depicts all the possible random outcomes and their probabilities. Green /" 3/8 \"Gree\\ 513 __+ R d 4I9 e 46 5 R 5/9 '15 R d 4f8 \"Green 418 \\Red Note: Please enter your answers below in fraction form. a) What is the conditional probability P(Red I Green) =? b) What is the probability of obtaining a nal outcome with two green objects? Question 15 2 pts The data gathered from an actual random sample of adults classied according to their gender and favorite way to eat ice cream are as follows: all =284 , c112 =169 , 4:113 =50 , c114 =38 , 115 =49 , 021 =468 , 122 =277 , 023 =23 , (124 =60 , C125 =60 The following contingency table was created based on the above data, where you will need to calculate the grand total, the total for each row, and the total for each column on your own before answering the question that appears after the table What is the probability that someone is female AND her favorite way to eat ice cream is in a sandwich. (For answers up to four decimal places, enter the number in the box below without rounding it. For answers that have more than four decimal values, round your answer to four decimal places). The data gathered from a survey of a random group of people about their smoking habits and their bodilyweights are: 6111 =151, an =192 , c113 =11 , am =294 , an 2311 , a23 =39 , 6131 2360 , 132 2215 , 6133 =16 , (141 2128 , 142 2204 , 143 =38 , 6151 2422 , (.152 = 1,580 , (.153 =78 The following contingency table was created based on the above data, where you will need to calculate the grand total, the total for each row, and the total for each column on your own before answering the question that appears after the table. -- "M _ Calculate the probability of someone who is a very heavy smoker, given that the individual is underweight (For answers up to four decimal places, enter the number in the box below without rounding it. For answers that have more than four decimal values, round your answer to four decimal places). Question 17 2 pts The data gathered from a survey of a random group of undergraduate university students about theiracademic standing are: 011 :71, 012 :86 , c113 =177 , 5114 :27 , (121 =1,214 , (122 =913 , (123 =722 , (124 =649 , (I31 =562 , G32 =239 , 133 =175 , (134 = 45 The following contingency table was created based on the above data, where you will need to calculate the grand total, the total for each row, and the total for each column on your own before answering the question that appears after the table. Academic _ _ Sophomore Junior Total Standing Probation Satisfactory Total What is the probability that a student is a "Sophomore" m has "Satisfactory" academic standing ? (For answers up to four decimal places, enter the number in the box below without rounding it. For answers that have more than four decimal values, round your answer to four decimal places). Question 18 2 pts The data gathered from a survey of a random group of cyclists and the routes they prefer are categorized in terms of a cyclist's gender and preference as follows: an :84, an :76 , (113 = 96 , 021 =62 , 122 =105 , 6123 =58 The following contingency table was created based on the above data, where you will need to calculate the grand total, the total for each row, and the total for each column on your own before answering the question that appears after the table. Calculate the probability of a cyclist being female, given that the cyclist prefers a wooded path (For answers up to four decimal places, enter the number in the box below without rounding it. For answers that have more than four decimal values, round your answer to four decimal places)