What is not an acceptable form of proof
1 answer:
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Answer:
(a) P(A) = 0.34
(b) P(B) = 0.33
(c) P(C) = 0.33
(d) The Complement of event A = 1 - P(A) = 0.66
Step-by-step explanation:
We are given that 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.
Let the probability that roommate A chooses rock = P() = 0.36
The probability that roommate A chooses paper = P() = 0.32
The probability that roommate A chooses scissors = P() = 0.32
The probability that roommate B chooses rock = P() = 0.22
The probability that roommate B chooses paper = P() = 0.25
The probability that roommate B chooses scissors = P() = 0.53
(a) Let A = event that roommate A wins the game and thus does not have to wash the dishes.
This will happen only when roommate A chooses rock and roommate B chooses scissors or roommate A chooses paper and roommate B chooses rock or roommate A chooses scissors and roommate B chooses paper.
So, P(A) =
= (0.36 0.53) + (0.32
0.22) + (0.32
0.25)
= 0.1908 + 0.0704 + 0.08
P(A) = 0.34
(b) Let B = event that roommate B wins the game and thus does not have to wash the dishes.
This will happen only when roommate B chooses rock and roommate A chooses scissors or roommate B chooses paper and roommate A chooses rock or roommate B chooses scissors and roommate A chooses paper.
So, P(B) =
= (0.22 0.32) + (0.25
0.36) + (0.53
0.32)
= 0.0704 + 0.09 + 0.1696
P(B) = 0.33
(c) Let C = event that the game ends in a tie.
This will happen only when roommate A chooses rock and roommate B also chooses rock or roommate A chooses paper and roommate B also chooses paper or roommate A chooses scissors and roommate B also chooses scissors.
So, P(C) =
= (0.36 0.22) + (0.32
0.25) + (0.32
0.53)
= 0.0792 + 0.08 + 0.1696
P(C) = 0.3288 ≈ 0.33
(d) The complement of event A = P(A') = 1 - P(A)
= 1 - 0.34 = 0.66.