Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Another Coin Flipping Question

  1. Sep 17, 2015 #1
    A random number p such that 0<p<1 is selected at random from a uniform distribution U[0,1]. A biased coin is then constructed such that the probability of heads on a single flip is p (thus 1-p for a tails).

    This coin is flipped twice and the result is HH. If the coin is flipped a third time, what is the probability of a third head? More precisely, what is the fair value of a lottery ticket that pays one dollar if the third flip is a head, and zero otherwise? What would you pay for it/ sell it for?
     
  2. jcsd
  3. Sep 17, 2015 #2

    DEvens

    User Avatar
    Education Advisor
    Gold Member

    Is this a trick question?

    "A biased coin is then constructed such that the probability of heads on a single flip is p..."
     
  4. Sep 17, 2015 #3
    not at all! I think it's well defined isn't it?
     
  5. Sep 17, 2015 #4

    DEvens

    User Avatar
    Education Advisor
    Gold Member

    Then the two H results don't give you any additional information. You know the probability is p, and you know the expected value of a $1 bet is p x $1.
     
  6. Sep 17, 2015 #5
    The question is asking for the probability of a third head PRIOR to finding out what p is.
     
  7. Sep 17, 2015 #6

    BWV

    User Avatar

    the bet is worth $0 as the probability of drawing a rational number from the uniform distribution is zero and you can't pay someone and irrational number's worth of currency ;)
     
  8. Sep 17, 2015 #7
    Ok for you we round p to the nearest 1/100. You still have to do the question now!
     
  9. Sep 18, 2015 #8

    gill1109

    User Avatar
    Gold Member

    We want to know the probability of HHH given HH. It's Prob(HHH) / Prob(HH). The probability of HHH is the expectation value of p^3 where p is uniformly distributed on the interval [0, 1]. So it's int_0^1 p^3 dp = 1/4. Similarly Prob(HH) = int_0^1 p^2 dp = 1/3. So the answer is 3/4.
     
  10. Sep 18, 2015 #9
    Looks right to me
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Another Coin Flipping Question
  1. Coin flipping (Replies: 6)

  2. Coin flip (Replies: 3)

  3. Flipping coin (Replies: 8)

Loading...