The Energy Council of a western state consists of four people, two of who are in favor of nuclear power generation, two opposed. The governor must select two members from the council to represent their state at a regional energy-planning conference. The two representatives are chosen at random by the governor.

List the simple events contained in the following events:
S: The sample space
A: Exactly one pro-nuclear power council member is chosen as a representative
B: Exactly two pro-nuclear power council members are chosen
C: Both anti-nuclear power council members are chosen.

(a) S: Sample space is all possible events. Sample space equals 12.
(b) Find the probabilities of events A, B, C, AB, AC, and AUB.

(b) Probability of event A is 67%.
Probability of event B is 17%.
Probability of event C is 17%.

Probability of event AB is 2 of 12 or 17%.
Probability of event AC is 2 of 12 or 17%.
Probability of event AUB is [P(A) + P(B)] – P(AB); (.67+.17)-.17 = .67

Any advice would be greatly appreciated.

Thank you.

ebaines

I'll help you with a couple to get you started, then you can do the rest.

There are 4 ways the two representatives for the conference can be chosen:

Pro, Pro
Pro, Anti
Anti, Pro
Anti, Anti

So, the probability of event A (exactly 1 pro is chosen) is 2/4, or 50%

When they ask what is the probability of AC, I take that to mean what is the probability of event A and event C occurring together, that is P(A&C) - is that right? If so, then the question can be stated: what is the probability of exactly 1 Pro being chosen (which means that one Anti is also chosen) and exactly 2 Antis being chosen (i.e. no Pros)? Clearly that's impossible, so the P(A&C) is 0.