1. Two roommates, roommate A and roommate B, are about to go cruising with a mutual friend and are arguing over who gets to sit in the front seat. Roommate A suggests a game of rock-paper-scissors to settle the dispute.

Question

Consider the game of rock-paper-scissor to be a probability experiment. How many outcomes are in the sample space of this probability experiment?
Is it 9?
Assume that both roommates' choices of rock, paper, or scissors are random, independent, and equally likely. Let Ra, Rb, Pa, Pb, Sa, and Sb denote roommate A choosing rock, roommate B choosing rock, roommate A choosing paper, etc. Additionally let the outcome consisting of roommates A and B both selecting rock be denoted parenthetically as (Ra, Rb), and so on for the other possibilities.

Define event A as the event that roommate A wins the game and gets to sit in the front seat.
Event is composed of what sample points?
a. A = {(Ra, Sb), (Pa, Rb), (Sa, Pb)}
b. A = {(Pa, Rb), (Sa, Pb)}
c. A = {(Ra, Rb), (Ra, Sb), (Pa, Rb), Sa, Pb)}
d. A = {(Ra, Pb), (Pa, Sb), (Sa, Rb)}

I'm really unsure, because I feel like it could be more than one of those.

Answer 1

(continued...) I think the answer for the last question above is A...
So,
What is the probability of event A?
a. .03
b. .90
c. .33
d. .67
Not sure at all
Let event C be the event that the game ends in a tie.
Event C is composed of what sample points?
a. C = {(Ra, Rb), (Ra, Pb), (Pa, Pb), (Sa, Pb), (Sa, Sb)
b. C = {(Ra, Rb), (Ra, Pb), (Ra, Sb), (Pa, Rb), (Pa, Pb), (Pa, Sb), (Sa, Rb), (Sa, Sb)}
c. {(Ra, Rb), (Pa, Pb), (Sa, Sb)}
d. {(Ra, Rb), (Ra, Pb), (Ra, Sb), (Pa, Rb), (Pa, Pb)}
It seems like C is the obvious choice, but I'm not sure if its supposed to be like a trick question or something

What is the probability of event C?
a. .25
b. .33
c. 0
d. .03
Is it B?

Lastly,
These probabilities were assigned using the
a. empirical method
b. subjective method
c. theoretical method
I think it is A.

Answer 2

Actually, I think it is C (theoretical), not A (Empirical)