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exam P easy question- Guo

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  • NoMoreExams
    replied
    Originally posted by Mysc View Post
    p40 in Guo Manual Problem 6

    "You first toss a coin. If you get heads, then you throw a die; if you get tails, then you toss another coin"

    Find
    (3) The probability that you get heads and the number 6

    I thought the answer would be 1/12, since the probability you get heads is 1/2, so (H,1)+(H,2)+(H,3)+(H,4)+(H,5)+(H,6)=1/2, so each one being equally likely, they would each have a probability of 1/12.
    But the manual says the probability is 1/8, since there are 8 possible outcomes, and they are all equally likely.
    Is this correct?
    If so, how does it relate to all the heads outcomes adding up to 1/2?
    After some discussion with some people we came up with a way to get 1/8. Assuming they mean if you flip heads you toss a die and if you flip tails, you flip heads and then allow one more toss of the die, then you get 1/8.

    Calculations:

    Flip H -> Roll a 6 = 1/2 * 1/6 = 1/12

    Flip T -> Flip H -> Roll a 6 = 1/2 * 1/2 * 1/6 = 1/24

    Therefore 1/12 + 1/24 = 3/24 = 1/8

    We did agree that this problem is horribly worded since what's stopping us from doing more flips if we get for example 2 tails, then we get the sequence

    Flip T -> Flip T -> Flip H -> Roll a 6, etc.

    If we continue in this fashion then we get the geometric sum:

    \sum_{i=1}^{\infty} \frac{1}{6} (\frac{1}{2})^{n} which converges to 1/6

    Feel free to comment on our solution.

    Leave a comment:


  • Gardo_Gomez
    replied
    Thought I had it.
    Last edited by Gardo_Gomez; July 30 2008, 05:53 PM. Reason: Miscalculate

    Leave a comment:


  • cmichener
    replied
    I'm going to bump this thread because I think this is interesting. Do any newer posters have a take on this?

    Leave a comment:


  • Guest's Avatar
    Guest replied
    This is really interesting, and I totally agree with you guys.I thought that the fact that we have two separate probabilities would make the answer anything but 1/8:

    Leave a comment:


  • Mysc
    replied
    thanks

    Thanks, it right at the beginning of the course, and I didn't understand what was wrong. I didn't hear back from the writer as of yet.

    Leave a comment:


  • Ken
    replied
    Originally posted by Mysc
    p40 in Guo Manual Problem 6

    "You first toss a coin. If you get heads, then you throw a die; if you get tails, then you toss another coin"

    Find
    (3) The probability that you get heads and the number 6

    I thought the answer would be 1/12, since the probability you get heads is 1/2, so (H,1)+(H,2)+(H,3)+(H,4)+(H,5)+(H,6)=1/2, so each one being equally likely, they would each have a probability of 1/12.
    But the manual says the probability is 1/8, since there are 8 possible outcomes, and they are all equally likely.
    Is this correct?
    If so, how does it relate to all the heads outcomes adding up to 1/2?

    I guess your manual is saying (H,1), (H,2),(H,3),(H,4),(H,5),(H,6),(T,H),(T,T) are all equally likely. I'd also disagree with that and say that P(H,6)=.5/6=1/12

    Leave a comment:


  • Mysc
    started a topic exam P easy question- Guo

    exam P easy question- Guo

    p40 in Guo Manual Problem 6

    "You first toss a coin. If you get heads, then you throw a die; if you get tails, then you toss another coin"

    Find
    (3) The probability that you get heads and the number 6

    I thought the answer would be 1/12, since the probability you get heads is 1/2, so (H,1)+(H,2)+(H,3)+(H,4)+(H,5)+(H,6)=1/2, so each one being equally likely, they would each have a probability of 1/12.
    But the manual says the probability is 1/8, since there are 8 possible outcomes, and they are all equally likely.
    Is this correct?
    If so, how does it relate to all the heads outcomes adding up to 1/2?
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