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Need a stats wiz… Simple question…

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  • March 20, 2007 at 3:10 pm #46470

    Anderson
    ★ 10 Years ★
    Participant

    How do I figure out the probablitiy of getting at least (1) heads when flipping a coin (3) times? (given that the prob. of getting a heads on one flip is 50%)
    I can’t seem to remember how to do this…
    Thanks,
    -Mike
     

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    March 20, 2007 at 3:28 pm #153627

    anonimus
    ★ 10 Years ★
    Participant

    the events could be
    H H H;  HHC; HCC ; CCC.   3 opportunity on 4
     the probability you can get at least one Head is = .75
     
     

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    March 20, 2007 at 3:51 pm #153629

    Cone
    ★ 10 Years ★
    Participant

    This is a binomial problem and your answer is wrong because you did not account for the number of ways some thing can happen
    0 heads can only happen one way and the probability is 0.125
    1 head can happen three different ways (HTT,THT, or TTH) and the probability of each is 0.125 for a total of 0.375
    2 heads can happen three different ways (HHT,HTH, or THH) and the probability of each is 0.375
    3 heads can only happen one way and the probability is 0.125.
    So the probability of 1 or more heads = 1- probability of 0 heads = 0.875.

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    March 20, 2007 at 4:32 pm #153633

    Bower Chiel
    ★ 10 Years ★
    Participant

    As with many probability probability problems this one may be solved quickly by looking at the complementary event to the one that you are interested in.P(At least one head)
    =1-P(No heads)
    =1-P(All three coins show tails)
    =1-0.5*0.5*0.5
    =0.875Sorry anonimus but I think you should have listed: –
    HHH HHT HTH THH HTT THT TTH TTT.Bower Chiel

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    March 20, 2007 at 4:57 pm #153636

    jediblackbelt
    ★ 10 Years ★
    Participant

    Maybe I am reading his question wrong, but I read it as if I flip a coin 3 times what is the probability that only one of them is heads.  If that is the case then wouldn’t you use the binomial probability? 
    I come up with a .375 chance that flipping a coin 3 times that only 1 of the coin flips will be heads. 
    Am I off base?

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    March 20, 2007 at 5:41 pm #153640

    Cone
    ★ 10 Years ★
    Participant

    Look at the words “at least” in the original problem.

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    March 20, 2007 at 5:48 pm #153643

    BritW
    ★ 10 Years ★
    Participant

    If it matters at this point – Gary is right.  Probability of filpping at least 1 head = 1-P(flipping 0 heads) = 1-.125 = .875.
    =1-{(3!/(0!(3-0)!)) x .5(to 0 power) x .5(to 3-0 power)}
    =1- {(1) x (1) x .125}
    = .875

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    March 20, 2007 at 6:51 pm #153649

    Anderson
    ★ 10 Years ★
    Participant

    Thanks for the replies.  I used the 1-p approach, but when I changed the probability of getting a heads to 20% (instead of 50%) my probability of getting at least one heads on three flips went up… which doesn’t make sense.
    (.5 x .5 x .5) = .125 = 1-p = 1-.125 = 87.5%
    (.2 x .2 x .2) = .008 = 1-.008 = 99.2%
    What am I doing wrong?
     

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    March 20, 2007 at 6:54 pm #153650

    Cone
    ★ 10 Years ★
    Participant

    It’s 1 – probability of three tails which is 1 – .8*.8*.8 or .488.

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    March 20, 2007 at 6:57 pm #153651

    BTDT
    ★ 10 Years ★
    Participant

    Mikea:In your second calculation you should use three p(tails) and subract from unity. You used three p(heads).Cheers, BTDT

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    March 20, 2007 at 7:00 pm #153652

    Anderson
    ★ 10 Years ★
    Participant

    Doh. Ok.. I feel like an idiot… not the first time either. Thanks all. =o)

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    March 20, 2007 at 10:31 pm #153663

    jediblackbelt
    ★ 10 Years ★
    Participant

    Cool.  Not off base, just misread.  Good thing this isn’t a stats test.  Thanks for the clarification.
     

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    March 21, 2007 at 3:28 am #153670

    goodie
    ★ 10 Years ★
    Participant

    MikeA,
    the diagram would be:
     
    1st flip                      H                                        T
    2nd flip            H              T                          H             T
    3rd flip       H       T       H       T               H      T      H     T  
                  HHH HHT HTH HTT           THH THT  TTH  TTT
    combination with at least 1 H is 7 out of 8, so
    the probability of having at least 1 Head is 7/8 = .875
     
    Goodie

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