Assignment 1 (10 Marks) Question 1 Study P(Study^Cheat APass) Pass ~Pass a) Compute whether cheat and pass conditionally independent given study. Show all calculations. b) Compute p(Pass or Cheat). P(Cold^Cloudy ^Rain) Cold ~Cold Cheat .25 .02 Cricket Football Other ~Cheat 15 .03 Question 2 Cloudy "Rain .06 .04 Question 3 Left-Handed .24 .15 .15 ~Study Cheat .10 .22 Rain .32 12 a) Compute the marginal probability of ~Cold. b) Compute the probability of not cloudy given the it is not raining and the weather being not cold c) Compute the probability of not raining given it is not cloudy. d) Compute P(~Rain or cloudy) Rain .26 .10 ~Cloudy ~Cheat 13 Right-Handed .1 .1 .26 .10 Rain .03 .07 a) Compute the probability of playing football for a left-handed person b) If someone plays Cricket, estimate the probability of being right-handed c) Compute the probability of playing Football and Cricket d) Compute the probability of being right-handed or left-handed e) Infer whether playing football depends on being Right-Handed Question 4 A Lie detector machine can correctly detect 96% of the time if a person tells a lie and correctly detect 95% of the time if a person tells a truth. In a jury board, the probability of a person telling a lie is 2%. Now, the lie detector machine declares that a person has told a lie. a) What is more likely, the person is a liar or not? Apply proper theorem and show full calculation. b) What is the probability of the person not being a liar? Apply proper theorem and show full calculation