math 157

An experiment has three possible outcomes: A, B, and C. If P(A)= P(B)and P(C)= 2P(A), what is the probability of each?

Can anyone help me get started?

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asked by Rmz
  1. Consider that P(A) + P(B) + P(C) = 1.

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    posted by Marth
  2. What do you mean?

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    posted by Rmz
  3. The sum of the probabilities of each outcome must equal 1. Therefore, you can find the probability of any outcome by algebra.

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

    I'll start you off.

    Let x = P(A).

    "P(A)= P(B)and P(C)= 2P(A)"

    Then x = P(B) and 2x = P(C).

    x + x + 2x = 1

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    posted by Marth
  4. So say I got x=1/4 would I substitute it in for P(A through C)?

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    posted by Rmz
  5. Yes. x = 1/4, so P(A) = x = 1/4. Similarly, you can find P(B) and P(C).

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    posted by Marth
  6. Alright I think I got it

    P(A)= 1/4
    P(B)= 2/5
    P(C)= 5/14

    RIght?

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    posted by Rmz
  7. Really good work.

  8. "P(A)= P(B)and P(C)= 2P(A)"

    We found that P(A) = x = 1/4. Therefore, P(B) = P(A) = x = 1/4.

    P(C) = 2P(A) = 2x = 1/2

    You can see that P(A) + P(B) + P(C) = 1/4 + 1/4 + 1/2 = 1

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    posted by Marth

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