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#4
anyway, let me go on:
so the next one, u want at least 3 to show heads.
so you basically want to know what the probability that 3 out of 4 will show heads OR all will be heads.
for all heads, it's easy. there is only one way to get all heads: TTTT. each coin that is tossed has a 1/2 probability of being heads. since there are 4 coins, (1/2)(1/2)(1/2)(1/2) = 1/16
for 3 heads, you have to note that there are 4 ways of getting this:
1) HTTT
2) THTT
3) TTHT
4) TTTH
this one is easy to see, but this is when you would use combinations. if you do the combination C(4,3) since u want 3 heads out of 4 you will get 4. note that C(4,3) is the same as C(4,1) since it is the same as the combinations when there is 1 T out of 4, as u can see in the list above. in notation, C(n,k) = C(n,n-k)
anyway, that's all the combinations of getting 3 heads. now you have to compute the probability. for each combination, it's the same. since the probability of heads = probability of tails = 1/2, it's (1/2)(1/2)(1/2)(1/2) again, or 1/16. then remember, there were 4 different ways, so 4/16.
so the probability of at least 3 heads = probability of all heads + probability of 3 heads = 1/16 + 4/16 = 5/16
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04-11-2003 05:28 AM
