Question

1. Consider the experiment of rolling a pair of dice values showing on the dice. experiment of rolling a pair of dice. Suppose we are interested in the sum of face a. How many simple events are possible? b. List the sample space. c. What is the probability of obtaining a 7? d. What is the probability of obtaining a value of 9 or more? Because each roll has six possible even values (2.4,6,8,10,12) and five possible odd values (3,5,7,9,11), the dice should show even values more often than odd values. Do you agree with this statement? Explain. e. Becam 2. Using the below table: B B: 0.4 0.2 0.1 a. Compute P(A, or B). b. Compute PCA, or B). c. Calculate the marginal probabilities from the following table of joint probabilities. d. Determine P(AB). e. Determine P(A B ). f. Did your answers to parts (a) and (b) sum to 1? Is this a coincidence? Explain. g. Calculate P( A B ). h. Calculate P(A2B). i. Are the events independent? Explain 3. Suppose there are 100 students in your accounting class, 10 of whom are left-handed. a. Two students are drawn at random. Draw the probability tree and insert the probability for each branch. What is the probability of the following events? b. Both are right-handed? c. Both are left-handed? d. One is right-handed and the other is left-handed? e. At least one is right-handed? 4. Suppose you flip eight fair coins. a. What is the probability of flipping exactly eight heads? b. What is the probability of flipping at least four heads? c. What is the probability of flipping at most seven heads? d. What is the probability of flipping less than three heads? e. What is the probability of flipping more than one head?

Answer 1

*(1) Rolling a pair of dice. (a) Number of are possible wents 6x6 136 events (6 sample space : - 9 0,0 (1,2)(1,3) Clu) (5) (1,6),(2,0 (232)(3,3) (2, 4) (2,5) (2,6) (3, 1) (3, 2) (3,3) (3, 4) (3,5) (3,6) (8.1 (A2 (4, 3) (4,4) (4,5) (4,6) (5, 1) (5,2) (5,3) (5,4) (5,5) (5,6) (6, 1) (6,2) (6, 3) (6,4) (C) 65) (6,6)} = (ettaining 1) +66) (6, 1) (2,5) (5,2) (4,3) (3,4)} = 6 events. pCobtaining 7) = 36 = 1 1 / 1 (d) obtaining a or more » {(1,5) (5, 4) (6, 3) (3,67 (5,5) (4,6) (6,4) (5,6) (6,5) (6,6) } p(obtaining a oromore) = 10