Two 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 probability tree for this problem?

Two 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.A worker learned the skill successfully. What is the probability that he was taught by method A?

Two 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

Two 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 15% of the time (method A is used the other 85% of the time). The following notations are suggested:A—Method A is used.B—Method B is used.L—Spanish was learned successfully.A person learned Spanish successfully. What is the probability that he was taught by method A? 0.85 * 0.70 = 0.5950 0.70 (0.15 * 0.85)/(0.85 * 0.70 + 0.15 * 0.85) = 0.1765 (0.85 * 0.70)/(0.85 * 0.70 + 0.15 * 0.85) = 0.8235 (0.85 * 0.70)/(0.70 + 0.85) = 0.3839

A teacher administers three different versions of a test to his students. The two-way table shows the results. Find each probability.Grade Pass FailTestA 49 7B 46 6C 34 12a. P(pass | Test A)Probability: $\%$%​b. P(Test C | fail)Probability:  $\%$

A student, Kevin, has handed in all her coursework for CS2114, and wants to workout the chance she will get a distinction in CS2114. She asked 300 students whohave had distinctions in the past, and 100 of them said they handed in all theircoursework. She then asked 600 students who didn’t get distinctions in the past,and only 50 of them said they handed in all their coursework. Past experience showsthat only 15% of students who take CS2114 get distinctions(a) Calculate the prior probability of someone handing in all their coursework.(b) Using this prior and the information above, calculate using Bayes’ rule whatthe probability is that she will get a distinction?(c) If she didn’t hand in all her coursework what is the probability of getting adistinction?