We are given a table with data of 67 members of the US Senate in June 2012 and their affiliated political party and when they are up for reelection.Up for re-election:Democratic PartyRepublican PartyOtherNovember 201420130November 201610240What is the probability that a randomly selected senator is up for reelection in November 2016? What is the probability that a randomly selected senator is a Republican or is up for reelection in November 2014?Suppose that a member of the US Senate is randomly selected. What is the probability that the senator is up for reelection in November 2014, knowing that this senator is a Republican?

How many Members of the Senate are up for re-election each election cycle?Group of answer choices100 percent33 percent75 percent66 percentNone of these

The number of votes for each of 2 candidates in a local election is shown in the table below. The electorate is divided into 3 different wards.  Ward 1 Ward 2 Ward 3Candidate A 152 84 122Candidate B 100 64 110What is the probability that someone lives in Ward 3 given that they voted for candidate B?

How many senators are up for re-election every two years?Group of answer choicesone-halfone-sixthone-thirdall

Suppose that the handedness of the last 15 U.S. presidents is as follows:(i) 40% were left-handed (L)(ii) 47% were democrats (D)(iii) If a president is left-handed, there is a 13% chance that the president is a Democrat.What is the probability that a randomly chosen U.S. president is left-handed and a democrat? 0.40 * 0.47 = 0.1880 0.40 * 0.13 = 0.0520 0.47 * 0.13 = 0.0611 0.40/0.47 = 0.8510 0.40/0.13 = 3.0769 0.47/0.13 = 3.6154Question 2Select one answer.10 pointsTwo methods, A and B, are available for teaching Spanish. There is a 70% chance of successfully learning Spanish if method A is used, and a 85% chance of success if method B is used. However, method B is substantially more time consuming and is therefore used only 20% of the time (method A is used the other 80% of the time). The following notations are suggested:A—Method A is used.B—Method B is used.L—Spanish was learned successfully.Which of the following is the correct probability tree for this problem?Question 3Select one answer.10 pointsTwo teaching methods, A and B, are implemented for learning Spanish. There is a 70% chance of successfully learning Spanish if method A is used, and a 85% chance of success if method B is used. However, method B is substantially more time consuming and is therefore used only 20% of the time (method A is used the other 80% of the time). The following notations are suggested:A—Method A is used.B—Method B is used.L—Spanish was learned successfully.What is the probability that a randomly chosen person will learn Spanish successfully? P(L) = 0.20 * 0.85 = 0.1700 P(L) = 0.80 * 0.70 = 0.5600 P(L) = 0.80 * 0.70 + 0.20 * 0.85 = 0.7300 P(L) = 0.80 * 0.85 + 0.20 * 0.70 = 0.8200 P(L) = 0.80 * 0.20 + 0.70 * 0.85 = 0.7550Question 4Select one answer.10 pointsTwo methods, A and B, are available for teaching a certain industrial skill. There is an 80% chance of successfully learning the skill if method A is used, and a 95% chance of success if method B is used. However, method B is substantially more expensive and is therefore used only 25% of the time (method A is used the other 75% of the time). The following notations are suggested:A—Method A is used.B—Method B is used.L—The skill was learned successfully.Which of the following is the correct representation of the information that is provided to us? P(A) = 0.75, P(B) = 0.25, P(L | A) = 0.80, P(L | B) = 0.95 P(A) = 0.75, P(B) = 0.25, P(A | L) = 0.80, P(B | L) = 0.95 P(A) = 0.75, P(B) = 0.25, P(A and L) = 0.80, P(B and L) = 0.95 P(A | L) = 0.75, P(B | L) = 0.25, P(L | A) = 0.80, P(L | B) = 0.95 P(A and L) = 0.75, P(B and L) = 0.25, P(L | A) = 0.80, P(L | B) = 0.95

Suppose that the handedness of the last 15 U.S. presidents is as follows:(i) 40% were left-handed (L)(ii) 47% were democrats (D)(iii) If a president is left-handed, there is a 13% chance that the president is a Democrat.What is the probability that a randomly chosen U.S. president is left-handed and a democrat? 0.40 * 0.47 = 0.1880 0.40 * 0.13 = 0.0520 0.47 * 0.13 = 0.0611 0.40/0.47 = 0.8510 0.40/0.13 = 3.0769 0.47/0.13 = 3.6154