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3 years ago

Help thx!!!!!!!!!!!!!!!!!!!!!!!!!!

Mathematics

1 answer:

Kay [80]3 years ago

3 0

Answer:

Answer E

Step-by-step explanation:

If you think about it, the origin is just (0,0). Now, think which one is the closest to that. (0,1/2), or answer E, should be your assumption.

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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 si

Leokris [45]

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( $R_A$ ) = 0.36

The probability that roommate A chooses paper = P( $P_A$ ) = 0.32

The probability that roommate A chooses scissors = P( $S_A$ ) = 0.32

The probability that roommate B chooses rock = P( $R_B$ ) = 0.22

The probability that roommate B chooses paper = P( $P_B$ ) = 0.25

The probability that roommate B chooses scissors = P( $S_B$ ) = 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) = $P(R_A) \times P(S_B) + P(P_A) \times P(R_B) + P(S_A) \times P(P_B)$

= (0.36 $\times$ 0.53) + (0.32 $\times$ 0.22) + (0.32 $\times$ 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) = $P(R_B) \times P(S_A) + P(P_B) \times P(R_A) + P(S_B) \times P(P_A)$

= (0.22 $\times$ 0.32) + (0.25 $\times$ 0.36) + (0.53 $\times$ 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) = $P(R_A) \times P(R_B) + P(P_A) \times P(P_B) + P(S_A) \times P(S_B)$