Math

A biased coin lands heads with probabilty 2/3. The coin is tossed 3 times
a) Given that there was at least one head in the three tosses, what is the probability that there were at least two heads?
b) use your answer in a) to find the probability that there was exactly one head, give that there was at least one head in the three tosses.
here is what I tried

a) p(at least 2 h | 1 h) = p(at least 1h and at least 2 h)/p(at least one head 1h)
I get stuck here as to what numbers I put I know that p(no heads in toss 1)= 1- 2/3 = 1/3

I appreciate any help
Thanks

asked by Steve
  1. https://www.physicsforums.com/threads/probability-unfair-coin-toss-probably-pretty-easy.342119/

    posted by bobpursley
  2. I looked at this link and still cant get it

    posted by Steve
  3. Lets' do the the prob of each of the two events, then worry about the conditional probability.

    Let prob(A) be the prob(at least one head in the three tosses)
    = 1 - prob(no head three times)
    prob(head) = 2/3, prob(no head) = 1/3
    prob(A) = 1 - C(3,0)(1/3)^3 (2/3)^0 = 1/27 = 26/27

    let prob(B) be prob(at least two heads in 3tries)
    = prob(exactly 2) + prob(exactly 3)
    = C(3,2)((2/3)^2 (1/3) + C(3,3)(2/3)^3 (1/3)^0
    = 3(4/9)(1/3) + 1(8/27)(1)
    = 12/27 + 8/27 = 20/27

    so you have P(P|Q) = prob( P and Q)/prob(P)
    read as : prob( P given Q)
    carry on

    or

    There are only 8 outcomes, so lets list them and their probs
    HHH ----> (2/3)^3 = 8/27
    HHT ----> (2/3^2 (1/3) = 4/27
    HTH ----> (2/3)^2 (1/3) = 4/27
    THH ----> (2/3)^2 (1/3) = 4/27
    HTT ----> (2/3)(1/3)^2 = 2/27
    THT ----> (2/3)(1/3)^2 = 2/27
    TTH ----> (2/3)(1/3)^2 = 2/27
    TTT ----> (1/3)^3 = 1/27 , note that their sum is 1 , as needed.

    out of those with at least 1 head, which is a prob of 26/27, there are 4 cases of at least 2 H's , the sum of those = 8/27 + 3(4/27) = 20/27
    so prob(what you asked for) = (20/27) / (26/27) = 20/26 = 10/13

    posted by Reiny

Respond to this Question

First Name

Your Response

Similar Questions

  1. Math

    A biased coin lands heads with probabilty 2/3. The coin is tossed 3 times a) Given that there was at least one head in the three tosses, what is the probability that there were at least two heads? b) use your answer in a) to find
  2. Math

    A biased coin lands heads with probabilty 2/3. The coin is tossed 3 times a) Given that there was at least one head in the three tosses, what is the probability that there were at least two heads? b) use your answer in a) to find
  3. math

    a fair coin is tossed in the air 4 times. if the coin lands heads up the first three tosses, what is the probability the coin will land heads up the fourth toss? I think it is 1/2 because the coin has 2 sides and 50% it will land
  4. Probability

    A coin is tossed 1000 times,out of which we observe 560 heads,the question of interest is whether the coin is biased or not?
  5. math

    an unbiased coin is tossed 3 times. find the probability that the coin lands heads exactly once.
  6. Math

    A biased coin is tossed 3 times. The probability that the coin will land on heads is 0.6 The probability that the coin will land on tails three times is less than 0.1 Is this correct? Show all your working.
  7. math

    an unbiased coin is tossed six times. find the probability of the given event. the coin lands heads more than once.
  8. math

    an unbiased coin is tossed six times. find the probability of the given event - the coin lands heads more than once.
  9. Maths

    The probability of a biased coin landing on heads is 0.6. I flip the coin 150 times, how many times would the coin land on heads?
  10. math

    Coin A is tossed three times and coin B is tossed two times. What is the probability that more heads are tossed using coin A than coin B? THE ANSWER IS NOT 7/16

More Similar Questions