Question

Please help me :) I will give you a shiny medal :3


A probability experiment is conducted in which the sample space of the experiment is
S={2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}, Event E = {2, 3, 4, 5, 6, 7} and event G= {9, 10, 11, 12} Assume that each outcome is equally likely. List the outcomes in E and G. Are E and G mutually exclusive?
E and G = {?}

I placed:

Answer 1

First I did:
E and G {2, 3, 4, 5, 6, 7, 9, 10, 11, 12}
But I got that incorrect...

Isn't it mutually exclusive? (Or disjointed?) such as P(E or G) = P(E) + P(G)?

Answer 2

@agent0smith I hope your not busy :>

Answer 3

Math doesn't read easily in paragraph form:

S={2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}

E = {2, 3, 4, 5, 6, 7}

G= {9, 10, 11, 12}

E and G = { } the empty set and thus they are mutually exclusive (there's zero overlap)

Answer 4

E and G means only the elements that show up in BOTH E and G, of which there are none.

What you did first is E or G, which is all of the elements in E and G, combined together.

Answer 5

P(E or G) = P(E) + P(G)
Yes this is true for mutually exclusive, since you'd normally use
P(E or G) = P(E) + P(G) - P(E and G)
but when two events are mutually exclusive, P(E and G) = 0, so
P(E or G) = P(E) + P(G) - 0

Answer 6

@agent0smith thank you so much for helping me understand! Sorry for the late reply, but it means a lot that you took time to help!