Need a stats wiz… Simple question…
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 This topic has 12 replies, 8 voices, and was last updated 15 years, 2 months ago by goodie.

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March 20, 2007 at 3:10 pm #46470
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
0March 20, 2007 at 3:28 pm #153627
anonimusParticipant@anonimus Include @anonimus in your post and this person will
be notified via email.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
0March 20, 2007 at 3:51 pm #153629This 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 = 0.875.0March 20, 2007 at 4:32 pm #153633
Bower ChielParticipant@BowerChiel Include @BowerChiel in your post and this person will
be notified via email.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)
=1P(No heads)
=1P(All three coins show tails)
=10.5*0.5*0.5
=0.875Sorry anonimus but I think you should have listed: –
HHH HHT HTH THH HTT THT TTH TTT.Bower Chiel0March 20, 2007 at 4:57 pm #153636
jediblackbeltParticipant@jediblackbelt Include @jediblackbelt in your post and this person will
be notified via email.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?0March 20, 2007 at 5:41 pm #153640Look at the words “at least” in the original problem.
0March 20, 2007 at 5:48 pm #153643If it matters at this point – Gary is right. Probability of filpping at least 1 head = 1P(flipping 0 heads) = 1.125 = .875.
=1{(3!/(0!(30)!)) x .5(to 0 power) x .5(to 30 power)}
=1 {(1) x (1) x .125}
= .8750March 20, 2007 at 6:51 pm #153649Thanks for the replies. I used the 1p 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 = 1p = 1.125 = 87.5%
(.2 x .2 x .2) = .008 = 1.008 = 99.2%
What am I doing wrong?
0March 20, 2007 at 6:54 pm #153650It’s 1 – probability of three tails which is 1 – .8*.8*.8 or .488.
0March 20, 2007 at 6:57 pm #153651Mikea:In your second calculation you should use three p(tails) and subract from unity. You used three p(heads).Cheers, BTDT
0March 20, 2007 at 7:00 pm #153652Doh. Ok.. I feel like an idiot… not the first time either. Thanks all. =o)
0March 20, 2007 at 10:31 pm #153663
jediblackbeltParticipant@jediblackbelt Include @jediblackbelt in your post and this person will
be notified via email.Cool. Not off base, just misread. Good thing this isn’t a stats test. Thanks for the clarification.
0March 21, 2007 at 3:28 am #153670MikeA,
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
Goodie0 
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