Question

2. Consider two dice, one red and one blue.
a. List the sample space of rolling the dice simultaneously.
b. Consider the events: A – Equal faces, B – Sum exceeds 9.
i. What is the probability of each event?
ii. Are these events mutually exclusive? Why or why not?

For a, I got {11, 12, ..., 16, 21, 22, ..., 66}. Please let me know if that's right. I mostly need help on b.

Answer 1

b - i. 1/6

Answer 2

How did you get that?

Answer 3

Probability of getting equal faces is 1/6. When we throw both the dice, we may obtain 1,1;1,2;1,3;1,4;1,5;1,6 or 2,1;..........
Probability of getting 1,1;2,2;3,3;4,4;5,5;6,6
is 6/36 which is 1/6

Answer 4

Ahh, I see now. What about for ii)? Is it mutually exclusive? How can I tell if it is or not?

Answer 5

What is mutually exclusive?

Answer 6

Probability of getting -Sum exceeds 9. is also 1/6

Answer 7

Mutually exclusive is something that occurs at the same time. I think it's something like that though.

Answer 8

Here is a better definition if you want (From dictionary.com):
of or pertaining to a situation involving two or more events, possibilities, etc., in which the occurrence of one precludes the occurrence of the other: mutually exclusive plans of action.

Answer 9

In layman's terms, two events are mutually exclusive if they cannot occur at the same time. An example is tossing a coin once, which can result in either heads or tails, but not both.
According to wikipedia

Answer 10

No, they are not mutually exclusive because 5,5 and 6,6 satisfy both

Answer 11

So that means that they both cannot occur at the same time correct?

Answer 12

No they can occur at the same time, 5,5 and 6,6
Read the definition again

Answer 13

Oh I see. I get it now. Thanks for helping me out. I really appreciate it. :)

Answer 14

Welcome