Question

1. Sheila has two six-sided dice- one is purple and the other is blue. She rolls both dice and observes the following outcome-if the purple die is 5 and the blue is 1 I might use the Y5G1 to denote the observation. A. How many outcomes come up doubles- both dice have the same number? B. How many possible outcomes are there for this observation? C. Find the probability that my observation is doubles. What contextual assumption do you need to make? D. How many outcomes have an even number on the blue die? What contextual assumption do you need to make? 2. I decide to play a game each morning with my uncle where I roll the two dice and pay my uncle $3 if its doubles or the blue die is even. But my uncle must pay me $5 dollars for any other observation occurs. a. If we play the game once each day in January, how much do I expect to have won or lost during the month? b. Find the expected value to me of this game c. Find the odds that my uncle wins the game on January 5

Answer 1

Q1) a) The number of outcomes which comes up doubles is computed to be 6 that is (1,1),(2,2),(3,3).... (6,6)

Therefore 6 outcomes is the required number of outcomes here.

b) Total outcomes possible here is computed as:
= Number of outcomes possible for first dice * Number of outcomes possible for second dice

= 6*6

= 36

Therefore 36 outcomes are possible here.

c) The probability of getting doubles is computed here as:

= (Number of doubles ) / Total number of observations

= 6/36

= 1/6

Therefore 1/6 is the required probability here.

The assumption required here is that each of the 36 outcomes here are equally probable.

d) Number of outcomes with even number on the blue die is computed here as:

= Number of even numbers on the blue die * Total number of outcome on the other die

= 3*6

= 18

Therefore 18 outcomes are here that satisfy the condition. Again the same assumption as previous case has been used here.