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.
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.
(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.
Actually, I think it is C (theoretical), not A (Empirical)
To determine which sample points are included in event A, we need to consider the outcomes that result in roommate A winning the game.
In a game of rock-paper-scissors, roommate A wins if:
- Roommate A chooses rock and roommate B chooses scissors (Ra, Sb)
- Roommate A chooses paper and roommate B chooses rock (Pa, Rb)
- Roommate A chooses scissors and roommate B chooses paper (Sa, Pb)
Based on this, the correct option for the sample points included in event A is:
a. A = {(Ra, Sb), (Pa, Rb), (Sa, Pb)}
Option b is incorrect because it does not include the possibility of roommate A choosing rock, and options c and d include sample points where roommate A loses the game.
To determine the sample space of this probability experiment, we need to consider all possible outcomes or combinations of choices between roommate A and roommate B.
In rock-paper-scissors, there are three possible choices: rock, paper, or scissors. Since each roommate has three choices, the total number of outcomes or sample points is the product of the number of choices for each roommate.
In this case, roommate A can choose rock, paper, or scissors, and roommate B can also choose rock, paper, or scissors. Thus, the sample space consists of all possible combinations of their choices.
To find the number of outcomes in the sample space, we multiply the number of choices for each roommate. Therefore, the correct answer is 3 choices for roommate A multiplied by 3 choices for roommate B, which gives us a total of 9 outcomes in the sample space.
Now, let's consider the event A, which represents the event that roommate A wins the game and gets to sit in the front seat. We need to determine which sample points are included in this event.
To determine the sample points in event A, we need to look for the outcomes where roommate A wins. In rock-paper-scissors, rock beats scissors, scissors beat paper, and paper beats rock.
From the given options:
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)}
In event A, roommate A wins if they choose paper (Pa) and roommate B chooses rock (Rb), or if roommate A chooses scissors (Sa) and roommate B chooses paper (Pb). Thus, the correct answer is option b: A = {(Pa, Rb), (Sa, Pb)}. These two sample points represent the outcomes where roommate A wins the game.
Therefore, event A is composed of {(Pa, Rb), (Sa, Pb)}.