Consider the probability experiment of rolling 2 dice. The outcomes from such an experiment are listed below, where each pair represents First Die, Second Die:

a. For the probability experiment, rolling 2 dice, what is the probability that we roll doubles?

b. Suppose you go to Coney Island and there is a game of chance based on rolling 2 dice. The cost to play the game is S3. You then roll the 2 dice and if you roll doubles you win a prize valued at S15. otherwise you lose. Set up the probability distribution for the random variable W, where W represents your winnings from the game.

c. For the game of chance in (c), the expected value of the game is -S0.50. Explain what this value tells us. How is this different from what you as an individual would see on a single play of this game?

d. Suppose you are asked to repeat the experiment (rolling 2 dice) 6 times. II we were interested in determining the probability that all 6 of those rolls of 2 dice would come up as doubles. one way we could go about solving the problem would be to treat this as a binomial process. Explain how we could use a binomial process to determine the probability that all 6 trials of this probability experiment would come up as doubles. You do not need to actually determine the probability value. (HINT: think about the properties a process has to possess to be classified as binomial.)

Transcribed Image Text:

1,1 1,2 2,1 2,2 W|N 1,3 2,3 3,3 3,1 3,2 4,1 4,2 4,3 5,1 5,2 5,3 6,1 6,2 6,3 1,4 2,4 3,4 4,4 4,5 1,5 W|N 55555 2,5 3,5 5,4 5,5 6,4 6,5 1,6 2,6 3,6 4,6 5,6 6,6 1,1 1,2 2,1 2,2 W|N 1,3 2,3 3,3 3,1 3,2 4,1 4,2 4,3 5,1 5,2 5,3 6,1 6,2 6,3 1,4 2,4 3,4 4,4 4,5 1,5 W|N 55555 2,5 3,5 5,4 5,5 6,4 6,5 1,6 2,6 3,6 4,6 5,6 6,6

Answer rating: 100% (QA)

a P roll doubles 63616 b Probability distribution of ... View the full answer