Assume you have a typical fair 6-sided die. That is to say, it has sides 1, 2, 3, 4, 5, 6 and each side has probability of 1/6 of occurring. You are to roll the die twice, and record the maximum, M, of the two 6 rolls. If you roll a 2 and a 3 (or a 3 and a 2), then M = 3. If you roll a 4 and a 4, then M = 4. The rolls are independent of each other. a. Derive the probability table for M. That is to say P(M = m) for m=1,2,3,4,5,6. b. Find the expected value of M, E(M)

You roll an 8-sided die. Let A = {4, 5, 7, 8} and B {1, 3, 6, 7}. Find the following. S = { 1,2,3,4,5,6,7,8 A' = {{ 1,2,3,6 B' = { 2,4,5,8 P(A') = P(B') = n(A OR B') = %3D n(A' AND B) %3D P(A OR B') = P(A' AND B) = P(A| B') = P(A' | B) = %3D

Solve Question 1 and show work. Please and thank you.

A poker player has either good luck or bad luck each time she plays poker. She notices that if she has good luck one time, then she has good luck the next time with probability 0.2 and if she has bad luck one time, then she has good luck the next time with probability 0.4. What fraction of the time in the long run does the poker player have good luck?

Becky and Carla take an advanced yoga class. Becky can hold 29% of her poses for over a minute, while Carla can hold 35% of her poses for over a minute. Suppose each yoga student is asked to hold 50 poses. Let B the proportion of poses Becky can hold for over a minute and C = the proportion of poses Carla can hold for over a minute. What is the probability that Becky's proportion of poses held for over a minute is greater than Carla's? Find the z-table here. O 0.159 O 0,259 0 0.448 O 0,741 Save and Exit Next Submit Math and rem 96 & 7 8 9. 10

Solve it fast and correctly. I will rate accordingly with multiple votes. Need 100% correct answer. There are eight seats at a rectangular table - three on each of the longer sides and one on each of the shorter sides. Six adults and two children sit around the table, with each seating configuration equally likely. What is the probability that the two children will end up seating next to each other on one of the longer sides of the table?

Please provide steps for how you got the solution to the problem provided below. A machine is used to produce one of each of two types of product (A and B) on alternating days, i.e., if A is produced today then B will be produced tomorrow and vice versa. Each day, there is a probability that the machine malfunctions. Malfunction probability after a day of operation is 0.03 when producing A and 0.07 when producing B. Once the machine malfunctions, it is no longer operable and will not be replaced until sometime in the future (beyond modeling horizon). Model the system as a Markov chain (give transition matrix on your paper). Suppose that on Monday product A was produced. Find the probability that the machine is still operable by the morning of Thursday. Your model should have a state ”malfunction”, which cannot transition to any other state other than itself.