Statistics play a large role in science. If I flipped this penny eight times, which of the following would be the least likely sequence? H=Heads T=Tails
A. HHTHTTHT
B. HHHHHHHH
C. THTHTHTH
I am delighted that this one stirred up so many comments. The idea came from a book I am reading, called "Am I Making Myself Clear?" The author, Cornelia Dean, was talking about the importance of understanding statistics in understanding science.
So, lets think about it, one step at a time. On the first flip, how likely are you to get heads? Its 50/50, right? What about for the second flip? Again, it is 50/50. So it is just as likely for you to get HH as it is for HT, TH, or TT. Now, on the third flip, what are the odds for getting heads? Again, 50/50, so the odds for HHH are the same as for HTH, HTT, TTH, THH, or TTT.
You can continue on, and no matter how many times you flip the coin, each time, you have a 50/50 chance of getting heads. That means that HHHHHHHH is just as likely as HHTHTTHT or any other combination.
Why does it seem that HHHHHHHH should be less likely? Because we expect random events to look random. This has too much pattern, so it seems less likely, but the odds of getting the exact sequence HHTHTTHT or any other exact squence is the same, 1 out of 256 possible combinations.
Great informative post!
Excellently)))))))
the nearly answer
the answer is not quite 1/2 but I carn't remenber what it is
...
Nice post, great looking blog, added it to my favorites!
not quite 50/50
on each side there is a different shape making one side more likely to land up than the other. It is a very very very small difference but if you flipped it thousands of times there would be a difference.
Sortov =
The side tails is slightly lighter than the heads side. There for the HHHHHHHH is slightly more likely than the other 2 listed, but if u where flipping a perfectly flat and perfectly cut coin then it would be 50/50 all the time.
The difference of heads vs tails is real small so you can still use coins to decide who goes first in games. Just bet on it being heads down! (unless they do the thing where they catch it and put it on there arm)
They have the same
They have the same probability
The probability of landing on heads is 1/2, as is the probability of landing on tails.
So no matter what the combinations are (as long as there are the same number of tosses of the coin) the probabilities will always be the same.
penny flipping
We're going with "B" because you have a 1 out of 2 chance to get any one side. Or in 8 tries, you would mostly likely get 4 heads and 4 tails in some kind of combination.
When we tried it, we got
Larisa: HHTTHHHH
Abbie: THHTHTHT
Danny: TTTTTHHT
Tacy: HHTHTHHH
Jon: TTTTTHHH
Mom: THTTHTTT
So, the odds were against our proving our own point. :-)
We think all the sequences
We think all the sequences would have the same likelihood.
B
Ethan Bailey
All are likely
As each side has the same probability of landing and each flip is independent of the last then all three answers are equally probable.
However, in all circulatory coins there will be some wear and this will be uneven so there will be a change in the movement in the air so that it has a higher chance of landing on one side or the other - this is more pronounced in 'loaded' coins.
Finally the way that the coin is flipped affects the way it lands - when I flip a coin that is heads up then more often than not it lands tails up.
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