Statistics/Probability

2. Two roommates, roommate X and roommate Y, are expecting company and are arguing over who should have to wash the dishes before the company arrives. Roommate X suggests a game of rock-paper-scissors to settle the dispute.
Consider the game of rock-paper-scissors to be a random experiment. In past games, roommate X has chosen rock 36% of the time, and roommate Y has chosen rock 22% of the time; roommate X has selected paper 32% of the time, and roommate Y has selected paper 25% of the time; roommate X has chosen scissors 32% of the time, and roommate Y has chosen scissors 53% of the time. (These choices are made randomly and are independently of each other.) Use these percentages to assign probabilities to the roommates' hand signal choices.
The probabilities were assigned using the
a. empirical method
b. theoretical method
c. subjective method
A?
Define event Y as the event that roommate Y wins the game and thus does not have to wash the dishes.
What is P'(Y), the probability of event Y?
a. .32
b. .33
c. .43
d. .22
I don't even know how I'm supposed to calculate that
Let event W be the event that the game ends in a tie.
What is P'(W), the probability of event W?
a. .32
b. .44
c. .55
d. .33
Again, idk!

  1. 👍
  2. 👎
  3. 👁
  1. Define event X as the event that roommate X wins the game and thus does not have to wash the dishes. What is the probability that roommate X wins the game?
    a. .34
    b. .37
    c. .67
    d. .43
    What is the complement of event Y?
    a. event Y or event W
    b. event X or event W
    c. event Y
    d. event W
    I think it is B
    The probability of the complement of event Y is
    a. .34
    b. .61
    c. .13
    d. .67

    1. 👍
    2. 👎
  2. A is correct.

    I assume you know that rock wins over scissors, paper wins over rock, and scissors wins over paper.

    For the other parts, make a tree diagram complete with corresponding probabilities and sum all the appropriate outcomes to get the probability.
    Example:

    R=rock, P=paper, S=scissors
    P(AB): probability that X chooses A, Y chooses B

    The probability tree for the complete game is as follows:
    cases
    1.P(RR)=0.36*0.22=0.0792
    2.P(RP)=0.36*0.25=0.0900
    3.P(RS)=0.36*0.53=0.1908
    4.P(PR)=0.32*0.22=0.0704
    5.P(PP)=0.32*0.25=0.0800
    6.P(PS)=0.32*0.53=0.1696
    7.P(SR)=0.32*0.22=0.0704
    8.P(SP)=0.32*0.25=0.0800
    9.P(SS)=0.32*0.53=0.1696
    Total probabilities=1.0

    For Y to succeed, add the probabilities P(RP)+P(PS)+P(SR)=0.0900+0.1696+0.0704
    =0.3300

    You can solve the remaining cases similarly.

    B is correct, because X,Y and W make the sample space and the probabilities should add to 1.

    The probability of Y' (complememnt of Y) , i.e. P(Y') can be obtained by subtracting P(Y) from 1.
    P(Y')=1-P(Y).

    1. 👍
    2. 👎
  3. Thanks a lot that made it simpler!
    So for the probability of W, would it be .32 or .33?

    Could you please look at my other posts as well and see if you can make them a little more clear for me please!

    Again, thanks a lot!

    1. 👍
    2. 👎
  4. And please disregard the probability of W question, It's .33 I'm pretty sure

    1. 👍
    2. 👎
  5. The sum
    P(RR)+P(PP)+P(SS)=0.3288 which rounds to 0.33.

    1. 👍
    2. 👎

Respond to this Question

First Name

Your Response

Similar Questions

  1. History

    Which accurately describes the purpose and history of the Virginia Company? The Virginia Company was a multinational company that received a royal charter from Spanish King Ferdinand II to trade slaves with the Virginia Colony.

  2. English

    All these sentences look right to me. Which is incorrect? Identify the incorrect sentence. A. The jury has been deliberating for the past three hours. B. Members of the jury have been deliberating for the past three hours. C. The

  3. Microeconomics

    Four roommates are planning to spend the weekend in their dorm room watching old movies, and they are debating how many to watch. Here is their willingness to pay for each film: Orson Alfred Woody Ingmar Frist film 7 5 3 2 Second

  4. History

    Why was the Dutch East India Company called a multinational corporation? 1 It was a Dutch company but only did business in Indian tea. 2 It was a Dutch company but was owned by monarchs of many European nations. 3 It was a Dutch

  1. English

    "If you've got it, (1)_____ it" That's the (2)_____ of Georgia's philosophy. Georgia is my dorm roommate. a dance and theater major, she is a true extrovert- always showing off, always "on stage". It seems she is in constant

  2. Business Communication

    Which of the following is an example of an external source? I. Memos sent to the employees of a company, 2. Financial reports published by a company, 3. Company databases, and 4. Industry journals.

  3. Physics

    Your roommate is working on his bicycle and has the bike upside down. He spins the 56.0 cm -diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What is the pebble's speed? What is the

  4. statistics

    A manufacturing company produces 10,000 plastic glasses per week. This company supplies plastic glasses to another company, which packages the glasses as part of picnic sets. The second company randomly samples 10 glasses from the

  1. Finance

    Omega Instruments has budgeted $300,000 per year to pay for certain ce- ramic parts over the next 5 years. If the company expects the cost of the parts to increase uniformly according to an arith- metic gradient of $1 0,000 per

  2. Vitamins

    Vitamins that may cause toxicity if ingested in too large amounts are: 1.vitamin A,vitamin C, and thiamin 2.vitamin C, riboflavin, and thiamin 3.vitamin A,vitamin D,and pyridoxin(B6) 4.vitamin D,vitamin C, and B12 Doesn't vitamin

  3. Physics

    A student weighing 800N crouches on a scale and suddenly vertically upward. His roommate notices that the scale reads 900 N momentarily just as he leaves the scale. With what acceleration does he leave the scale?

  4. Economics

    1. Your roommate's long hours in chem lab finally paid off--she discovered a secret formula that lets people do an hour's worth of studying in 5 minutes. So far, she's sold 200 doses and faces the following average-total-cost

You can view more similar questions or ask a new question.