May 4 2004 5.1, 5.2, 5.3 Discrete Probability Quiz 4 May 4 2004 5.1, 5.2, 5.3 Discrete Probability

Quiz 4: May-04 ’04 3.30-3.45 pm We conduct an experiment where we roll a die 5 times. The order in which the numbers a read out is important. What is the total number of possible outcomes of this experiment. b) What is the probability that exactly 3 times a “2” appears in the sequence (event E) (hint: first count the number of ways you can realize a sequence with 3 “2”’s, then count the number of each sequence can be realized.) c) What is the probability that at least twice no “2” appears, i.e. 1,3,4,5 or 6 appears (event F). This question will not be part of your grade. d) Which of the following are true: e) Compute the probabilities: f) Are the events E and F independent ?

Quiz 4: Answers What is the total number of possible outcomes of this experiment. 6^5 b) What is the probability that exactly 3 times a “2” appears in the sequence (event E) (hint: first count the number of ways you can realize a sequence with 3 “2”’s, then count the number of each sequence can be realized.) C(5,3) x 5^2 / 6^5 c) What is the probability that at least twice no “2” appears, i.e. 1,3,4,5 or 6 appears (event F): The probability that at most 3 times a “2” appears= 5^5/6^5 + C(5,1) x 5^4/6^5 + C(5,2) x 5^3/6^5 + C(5,3) x 5^2/6^5. prob. 0 “2”’s appear – prob. 1 “2” appears etc. until prob. 3 “2”’s appear. d) Which of the following are true: If E happens, then F is automatically true  E is subset of F. e) Compute the probabilities: , P(E|F) = P(E)/P(F), P(F|E) = P(E)/P(E) = 1 f) Are the events E and F independent ? NO!