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

Answer 1

Empirical formula

0.34

0.33

0.33

A^c = event B or event C

Explanation:

A = roommate A wins the game

P(A) = (Rock A and Scissors B) + (Scissors A and paper B) + (paper A and rock B)

P(A) = (0.36*0.53) + (0.32*0.25) + (0.32*0.22) = 0.3412

C = game ends in a tie :

P(C) = (RockA and rockB) + (ScissorsA and ScissorsB) + (ScissorsA and ScissorsB)

P(C) = (0.36*0.22) + (0.32*0.53) + (0.32*0.25) = 0.3288

P(B) = 1 - P(A) - P(C)

P(B) = 1 - 0.3412 - 0.3288

P(B) = 0.33

Complement of event A =event B or event C