Question

50 POINTS ANSWER ASAP!!!!!

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.
[Part A] Make a list of all the different possible outcomes when two number cubes are rolled.
[Part B] What fraction of the possible outcomes is favorable?
[Part C] Suppose you rolled the two number cubes 100 times, would you expect at least one 3 more or less than 34 times? Explain.
I'm a little bad at probabilities

Answer 1

[Part A] There are 36 possible outcomes when two number cubes are rolled. Here's the list:

1-1, 1-2, 1-3, 1-4, 1-5, 1-6
2-1, 2-2, 2-3, 2-4, 2-5, 2-6
3-1, 3-2, 3-3, 3-4, 3-5, 3-6
4-1, 4-2, 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, 6-5, 6-6

[Part B] There are 11 favorable outcomes (3-1, 3-2, 3-3, 3-4, 3-5, 3-6, 1-3, 2-3, 4-3, 5-3, 6-3) out of 36 possible outcomes. So the fraction of the possible outcomes that is favorable is 11/36.

[Part C] The probability of rolling at least one 3 in a single roll is 11/36. So the probability of not rolling any 3s in 100 rolls is (25/36)^100. Using a calculator, we get that this probability is about 0.0002. Therefore, we would expect to roll at least one 3 more than 34 times.