I'll try again. This time without python.
You throw two coins 1000 times. Each time, you write down the result. On average, you will then get roughly 250 heads-heads, 250 tails-tails, 250 heads-tails and 250 tails-heads. I hope we all agree on this.
You then select one of those results you just wrote down, and tell your friend that at least one of the coins came up heads in that throw. What is the probability that the other coin was also heads?
Well, since one of the coins was heads, you can disregard all the tails-tails results. That means that you could have one of the 250 heads-tails results, or one of the 250 tails-heads results, or one of the 250 heads-heads results. Hence, the probabilty that it was heads-heads is only 1/3.
Also, I don't know why this is relevant, but to get 1/3 from powers of 2, you can take (1/2^2)
1-1/2^2). Which is essentially what we are doing here.
You throw two coins 1000 times. Each time, you write down the result. On average, you will then get roughly 250 heads-heads, 250 tails-tails, 250 heads-tails and 250 tails-heads. I hope we all agree on this.
You then select one of those results you just wrote down, and tell your friend that at least one of the coins came up heads in that throw. What is the probability that the other coin was also heads?
Well, since one of the coins was heads, you can disregard all the tails-tails results. That means that you could have one of the 250 heads-tails results, or one of the 250 tails-heads results, or one of the 250 heads-heads results. Hence, the probabilty that it was heads-heads is only 1/3.
Also, I don't know why this is relevant, but to get 1/3 from powers of 2, you can take (1/2^2)
1-1/2^2). Which is essentially what we are doing here.Rather than a double count, it's a non-count of an already excluded case, leaving us with only 75% of all possible outcomes, and naturally 25/75=1/3. That would do it, on both "counts. " And it does make birth order irrelevant; you can just as easily treat it as 25% being boy, boy (or heads, heads) and 50% being one of each; it's still 25/75. My bad.
Honorbound and honored to be Bonded to Mahtaliel Sedai
Last First in wotmania Chat
Slightly better than chocolate.
Love still can't be coerced.
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Last First in wotmania Chat
Slightly better than chocolate.
Love still can't be coerced.
Please Don't Eat the Newbies!
LoL. Be well, RAFOlk.
Recreational mathematics
- 24/05/2010 09:17:27 PM
1113 Views
How is boy/girl different from girl/boy?
- 25/05/2010 01:05:15 AM
959 Views
I think it has to do with sequence
- 25/05/2010 08:37:05 AM
838 Views
The problem doesn't state the sequence, so there's no reason to assume it.
- 25/05/2010 08:56:09 AM
924 Views
Faulty "logic". 2/4
- 25/05/2010 02:12:54 AM
1000 Views
I was going to say.
- 25/05/2010 02:48:38 AM
851 Views
Yeah
- 25/05/2010 05:05:16 AM
817 Views
Re: Yeah
- 25/05/2010 09:52:58 AM
1042 Views
I don't know Python, but I think I know what went wrong there.
- 25/05/2010 11:33:18 AM
861 Views
Re: I don't know Python, but I think I know what went wrong there.
- 25/05/2010 01:53:01 PM
1015 Views
Ah, I see now; sorry.
- 25/05/2010 02:27:05 PM
820 Views
You realize this thread now contains the words "Monty" and "Python" several times, right? 
- 26/05/2010 11:01:24 AM
745 Views
- 26/05/2010 11:01:24 AM
745 Views