(Score for Question 1: of 5 points) 1.
In a board game, you must roll two 6-sided number cubes. You can only start the game if you roll a 3 on at
least one of the number cubes.
(a) Make a list of all the different possible outcomes when two number cubes are rolled.
(b) What fraction of the possible outcomes is favorable?
(C) Suppose you rolled the two number cubes 100 times, would you expect at least one 3 more or less
than 34 times? Explain.

Step-by-step explanation:

3  3

3  1

3  2

3  4

3  5

3  6

1   3

2  3

4  3

5  3

6  3

B

The number of favorable outcomes is 11 The probability of getting one of those outcomes is 11/36 . So the fraction you want is 11/36

C. In 100 throws, the outcome should be about 11/36 * 100 or about 31. That is too close to call. I'm going to try it with a million times and see what happens.

If I run this question a million times, I get 0.305 something. 100 is too small a sample to tell. I would expect it to be less than 34 times. If you run the simulation a million times, you get an answer that is very accurate to 3 places.

Even with a hundred times, you are going to get 34 or more very infrequently.

answer: expected value of x = 1.0

step-by-step explanation:

p(x=0) = 0.25

p(x=1) = 0.50

p(x=2) = 0.25

expected value for x = 0×0.25 + 1×0.5 + 2×0.25 = 1.0