IUPUI - Assignment Worksheet http://syrup.math.iupui.edu:8080/mapleta/modules/unproctoredT... Online Homework System 2/21/16 - 9:50:36 PM EST Name: ____________________________ Class: Rainey -- Spring 2016 -- 22333 MW 9:00AM Class #: ____________________________ Section #: ____________________________ Instructor: Joan Rainey Assignment: hw5 4.1-4.3 Assignment Instructions: You can enter fraction or decimal answers. Give several decimal places if you choose decimals. All of the following are acceptable formats for answers: 1/4 0.25 .25 0.312648 .312648 Question 1: (1 point) 5 , determine the odds in favor of event E. 13 (a) 13 : 5 If the Pr[E] = (b) 18 : 5 (c) 8 :5 (d) 5 :8 (e) 5 : 18 (f) 5 : 13 Question 2: (1 point) An experiment consists of ipping a fair coin 3 times. What are the odds in favor of obtaining at least one head? 7 (b) 1 (c) 1 (d) 7 (e) 1 (f) 2 (a) 1 of 7 : : : : : : 1 8 3 8 7 1 2/21/16, 9:51 PM IUPUI - http://syrup.math.iupui.edu:8080/mapleta/modules/unproctoredT... Question 3: (1 point) Let A and B be events such that Pr[A = 0.44 , Pr[B ]= 0.56 , and Pr[A B ]= 0.2 . Evaluate: Pr[AB] ____________ Pr[BA] ____________ Question 4: (1 point) Let C and D be events such that Pr[C = 0.58 , Pr[D ]= 0.51 , and Pr[C D ]= 0.88 . Evaluate: Pr[C| D] Pr[D| C] ____________ ____________ Question 5: (1 point) Given Pr[A = 0.41 and Pr[B| A ]= 0.37 , determine Pr[A B] . Question 6: (1 point) A pair of fair dice is rolled and the sum of the numbers is noted. Determine the probability that one die resulted in a 5 given that the sum is 8. Question 7: (1 point) Let E and F be events such that Pr[E = 0.57 , Pr[F ]= 0.5 , and Pr[E F ]= 0.27 . Evaluate: Pr(EF ) ____________ Pr(F E ) 2 of 7 ____________ 2/21/16, 9:51 PM IUPUI - http://syrup.math.iupui.edu:8080/mapleta/modules/unproctoredT... Question 8: (1 point) There are 4 women and 4 men on a committee. A subcommittee of three people is selected at random. What is the probability that all three people selected are women, given that all three selected are the same gender? Question 9: (1 point) Given the following tree diagram, determine Pr[B 3 of 7 E] 2/21/16, 9:51 PM IUPUI - http://syrup.math.iupui.edu:8080/mapleta/modules/unproctoredT... Question 10: (1 point) Given the following tree diagram, determine Pr[C| B] Question 11: (1 point) Given the following tree diagram, determine Pr[C] 4 of 7 2/21/16, 9:51 PM IUPUI - http://syrup.math.iupui.edu:8080/mapleta/modules/unproctoredT... Question 12: (1 point) An unfair coin with Pr[H = 0.3 is ipped. If the ip results in heads, a student is selected at random from a class of 9 boys and 12 girls. Otherwise, a student from a different class containing 11 boys and 8 girls is selected. What is the probability of selecting a girl ____________ What is the probability of selecting a girl, given that the ip resulted in heads? ____________ Question 13: (1 point) A test for colorblindness was conducted on 1,071 students in a high school. The results based on genders are shown in the following table Females Males Not Colorblind 510 527 Colorblind 12 22 What is the probability that a person selected at random is colorblind? ____________ What is the probability that a person selected at random is male and colorblind? ____________ What is the probability that a person selected is male given that the person is colorblind? ____________ Question 14: (1 point) The probability of a snowstorm on Thanksgiving is 0.32 and the probability of a snowstorm on Christmas is 0.55 . Assuming that these two events are independent: What is the probability of snowstorms on both Thanksgiving and Christmas? ____________ What is the probability of a snowstorm on either Thanksgiving or Christmas (or both)? ____________ What is the probability of a snowstorm on Thanksgiving but not on Christmas? ____________ Question 15: (1 point) Given Pr[E = 0.49 and Pr(EF) = 0.59 , determine Pr[F] If ____________ If ____________ 5 of 7 2/21/16, 9:51 PM IUPUI - http://syrup.math.iupui.edu:8080/mapleta/modules/unproctoredT... Question 16: (1 point) Given the following tree diagram, determine Question 17: (1 point) An unfair coin with Pr[H] = 2/3 is ipped. If the ip results in a head, then a marble is selected from an urn containing 2 red, 2 white, and 9 blue marbles. If the ip results in a tail then a marble is selected from an urn containing 5 red and 4 white marbles. If the marble selected is white, then what is the probability that a ip resulted in a head? Question 18: (1 point) A person holds a two-tailed coin in one hand and a fair coin in the other. A hand is chosen at random and the coin is ipped. If tails shows, what is the probability that it is the two tailed coin? Question 19: (1 point) A prisoner escapes from jail and randomly selects one of three roads leading away from the jail. Each of the roads leads to one of the three cities Atlanta, Boston, and Columbus. If he chooses the road to Atlanta, there is a 0.3 probability that his escape will be successful. If he chooses the road to Boston, there is a 0.4 probability that his escape will be successful. Finally, if he chooses the road to Columbus there is a 0.3 probability 6 of 7 2/21/16, 9:51 PM that his escape will be successful. If the prisoner is successful in his escape, what is the probability he selected the road to Atlanta? IUPUI - http://syrup.math.iupui.edu:8080/mapleta/modules/unproctoredT... Question 20: (1 point) The Centers for Disease Control (CDC) estimates that 0.5% of Americans have AIDS. The HIV-1 tests correctly diagnose the presence of HIV in 98.5% of the persons who have it and correctly diagnose its absence in 93% of the persons who don't. Find the probability that a person whose result is negative actually is negative. 7 of 7 2/21/16, 9:51 PM