1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
max2010maxim [7]
2 years ago
5

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

multaneously 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?
P(A) = 0.32
P(A) = 0.22
P(A) = 0.34
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?
Mathematics
1 answer:
Leokris [45]2 years ago
4 0

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)  

             =  (0.36 \times 0.22) + (0.32 \times 0.25) + (0.32 \times 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.

You might be interested in
I NEED HELP ill mark brainilist to best answer
Arturiano [62]
All you have to do is add up the side lengths we already know then subtract by the perimeter.
60.3 is the side lengths all together that we know
82-60.3=21.7
Hope this helped!!

4 0
2 years ago
Read 2 more answers
a backpack manufacturer produces an internal frame pack and an one hour and let y represent the number of external frame packs p
Flauer [41]
Are there answer choices i really dont under stand the question

7 0
3 years ago
What is the difference between proportional and nonproportional relationships?​
IceJOKER [234]

Answer:

If two quantities are proportional, then they have a constant ratio. If the ratio is not constant, the two quantities are said to be non-proportional.

3 0
2 years ago
Alan multiplies a 4-digit number by 36. How can you tell the
mafiozo [28]

The number of partial products Alan will have when he multiplies a 4-digit number by 36 is; 8 partial products.

First, we must establish that a 4-digit number will have 4 place values namely;

  • Thousands
  • Hundreds
  • Tens
  • Ones.

And since, 36 has 2 place values;

We can conclude that the number of partial products that Alan wil have is; 2× 4 = 8.

Read more on partial products;

brainly.com/question/705781

8 0
2 years ago
Read 2 more answers
4. (10 points) From the given triangle:
katrin2010 [14]

Answer:

sinθ =  y/r        sinθ = \frac{-6}{10} = \frac{-3}{5}

cosθ =  x/r       cosθ = \frac{8}{10} = \frac{4}{5}

tanθ =  y/x       tanθ =  \frac{-6}{8} =\frac{-3}{4}

cscθ =  r/y       cscθ = \frac{-5}{3}

secθ =  r/x       secθ =  \frac{5}{4}

cotθ = x/y       cotθ = \frac{4}{3}

explanation:

r = \sqrt{(8)^{2}+(-6)^{2}  }

r = 10

x = 8

y = -6

r = \sqrt{(4)^{2}+(3)^{2}  }

r = 5

x = 4

y = 3

7 0
3 years ago
Other questions:
  • Trisha needs to make at least 50 gift bags for an event. Each gift bag will contain at least 1 thumb drive or 1 key chain. She w
    5·2 answers
  • Use the remainder theorem to divide 5x^2+9x-2 by x+3. What is the remainder
    11·2 answers
  • If you begin investing at age 45 instead of age 40, how much more do you need to invest per month to have $retirement ? Why this
    15·1 answer
  • Evaluate 12 sigma n=3 -5n-1<br> −410<br> −385<br> 385<br> 410
    13·1 answer
  • Javier earned $820 dollars this week .he net income was $683.20.he paid $95.60 in federal income tax. How much did Javier pay in
    9·2 answers
  • Dustin's family is moving across town. They are busy packing their furniture into a moving van. The storage space in the moving
    15·1 answer
  • alejandro has 70 marbles. darius has M marbles. if alejandro has 10 times as many marbles does darius have?
    13·1 answer
  • Solve for the x using elimination <br> 3x-2y=13x−2y=1 <br> 2x+2y=42x+2y=4
    7·1 answer
  • Enter the coordinates of a point that is 5 units from (-2, -1). The coordinates of a point 5 units away is (-2, ).
    14·1 answer
  • Question<br> Find the value of x.<br><br><br><br> x=
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!