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Homework Help: M&Ms Probability help

  1. Jul 31, 2016 #1
    1. The problem statement, all variables and given/known data

    A bowl contains a large number of M&Ms. A single M&M is chosen at random, its colour is observed, and then it is returned to the bowl. A second M&M is chosen at random and its colour is observed. Let A be the event that the first M&M is yellow and B be the event that the second M&M is blue.
    i. Provide a reason why you think P(B|A) = P(B) is true or not.

    (d) An adult member of the Australian population is chosen at random. Let A be the event that chosen person was born in Australia and let B be the event that the person speaks more than one language.
    i. Provide a reason why you think P(B|A) = P(B) is true or not.

    3. The attempt at a solution

    not sure if this is correct:

    a) It is true as once you take it out you are putting it back in meaning that the probability is still the same

    b) it is not true as the probability of selecting someone who speaks another language in the Australian population is different to selecting a person who was born in Australia and speaks another language
  2. jcsd
  3. Jul 31, 2016 #2
    a) I agree with your answer.
    b) Although I don't have statistics to back it up, I think it is probably true that the percentage of the population that speaks more than one language varies depending on where one is born. So I agree with you on b also.
    EDIT: I want to change "probably true" to "almost certainly true" for part b.
  4. Jul 31, 2016 #3


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    This is a bit tricky. It depends how the probability distribution is defined.

    If it means the distribution based on the actual numbers of each colour in the pot (even if you do not know these numbers), you are right.

    But you could read the question in terms of your own estimate of the probability without knowing what the actual numbers are. In this case, you would need to consider that you have an a priori belief about what the numbers might be. Whatever probabilities you assign to those possible distributions, the fact that you drew a yellow one the first time should shift those estimates in favour of distributions with more yellows. Consequently, your estimate of the likelihood of picking a blue next decreases slightly.
    If you have heard of Bayesian statistics, you should seriously consider this interpretation.
  5. Aug 3, 2016 #4
    You're correct. This is a problem to test your understanding of independence. In probability, two events(A,B) are said to be independent if P(B|A)=P(B), that is, A and B have nothing to do with each other.


    Because the M&M is returned, choosing a yellow is independent of choosing a blue.

    b) Nationtionality has nothing to do with language plurality.
  6. Aug 3, 2016 #5
    Matthew314159271828 = MatthewPie :smile:
  7. Aug 3, 2016 #6


    Staff: Mentor

    I'm inclined to agree with Tom Hart. I don't have any statistics to back this up, but my sense is that if the person selected was not born in Australia, that person is more likely to speak another language than one who was born in Australia.
  8. Aug 3, 2016 #7
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  9. Aug 3, 2016 #8
    MatthewPie, I think we all appreciate that you used an abbreviated version for your username. :)
  10. Aug 3, 2016 #9
  11. Aug 3, 2016 #10


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    I feel sure that is the intended answer, but it's not quite that simple, for the reason I gave in post #3.

    It is reasonable to suppose that not all pots of M&Ms have the same blue:yellow ratio. The fact of getting a yellow the first time very slightly pushes the odds in favour of this pot having lower such ratio than average, so slightly depresses the odds of a blue next.
    Last edited: Aug 3, 2016
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