A,B,C, and D are all answer choices A common way for two people to settle a friv
ID: 3201519 • Letter: A
Question
A,B,C, and D are all answer choices
A common way for two people to settle a frivolous dispute is to
play a game of rock-paper-scissors. In this game, each person
simultaneously displays a hand signal to indicate a rock, a piece
of paper, or a pair of scissors. Rock beats scissors, scissors
beats paper, and paper beats rock. If both players select the
same hand signal, the game results in a tie.
Two roommates, roommate A and roommate B, are expecting
company and are arguing over who should have to wash the
dishes before the company arrives. Roommate A suggests a
game of rock-paper-scissors to settle the dispute.
Consider the game of rock-paper-scissors to be an experiment. In the long run, roommate A chooses rock 36% of the time, and
roommate B chooses rock 22% of the time; roommate A selects paper 32% of the time, and roommate B selects paper 25% of
the time; roommate A chooses scissors 32% of the time, and roommate B chooses scissors 53% of the time. (These choices are
made randomly and independently of each other.)
The probabilities were assigned using the
-------------------------
Define event A as the event that roommate A wins the game and thus does not have to wash the dishes.
What is P(A), the probability of event A?
a
P(A) = 0.32
b
P(A) = 0.22
c
P(A) = 0.34
d
P(A) = 0.38
Let event C be the event that the game ends in a tie.
What is P(C), the probability of event C?
a
P(C) = 0.44
b
P(C) = 0.33
c
P(C) = 0.55
d
P(C) = 0.25
Define event B as the event that roommate B wins the game and thus does not have to wash the dishes. What is the probability
that roommate B wins the game?
a
P(B) = 0.67
b
P(B) = 0.43
c
P(B) = 0.33
d
P(B) = 0.50
What is the complement of event A?
A^c= event A
A^c = event A or event C A^c = event B or event C
A^c = event C
The probability of N is
a
P(A) = 0.32
b
P(A) = 0.22
c
P(A) = 0.34
d
P(A) = 0.38
Explanation / Answer
Probability of A choosing Rock = PA(R) = 0.36
Probability of A choosing Paper = PA(P) = 0.32
Probability of A choosing Scissor = PA(S) = 0.32
Probability of B choosing Rock = PB(R) = 0.22
Probability of B choosing Paper = PB(P) = 0.25
Probability of B choosing Scissor = PB(S) = 0.53
What is P(A), the probability of event A?
Note: Choices of A are independent to that of B.
There are following possibilites of A winning,
PA = P1 + P2 + P3 = 0.1908+0.08+0.0704 = 0.3412
Answer: Option C
What is P(C), the probability of event C?
There are following possibilites of a Tie,
PC = P1 + P2 + P3 = 0.0792+0.1696+0.08 = 0.3288 = 0.33 (Approx.)
Answer: Option B
What is P(B), the probability of event B?
There are following possibilites of B winning,
PB = P1 + P2 + P3 = 0.0704+0.1696+0.09 = 0.33
Answer: Option C
What is the complement of event A?
The complement of A winning is either A losing (Event B) or a Tie (Event C).
Hence Ac = Event B or Event C