For those who saw Derren Brown or love arguing about probability (I'm

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greenbean1

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not a maths genuis, and need advice!!)? My husband and me are arguing over whether the example of which side the coin lands on, either heads or tails is the same as which pepper is pulled out of a bag containing 2 peppers, 1 red and 1 green, either red or green. I maintain it is more likely to get a run of the same colour or side, because there is a 1 in 2 chance of pulling a green pepper out just as there is a 1 in 2 chance of the coin landing on heads. My thoughts are that a mixture of red and green (or heads and tails) is more likely, because if pepper 1 is green, then pepper 2 is more likely to be red because this is still 1 in 2, whereas for it to be green, likelihood is against it, because the green pepper would now have to be a green-pepper-that-has-been-preceded-by-a-green-pepper, so this would be 1 in 2 x (the likelhood of this happening twice, I don't know the exact fraction because maths is really not my strong point). Anyway, am I right? That XXX or YYY is less likely than XXY or XYY or YYX or YXX or YXY or XYX- there is 2 of the first and 6 of the second, so surely these are more likely? I'm saying that the significance in Derren Brown's stunt is that the bloke had all outcomes the same whereas the woman's were mixed- there are only 2 combinations where everything is the same, whereas there are 6 combinations where outcomes are mixed.
 
i did not see brown.
for a fair coin the probability for each flip is independent of a previous flip.
the prob head = prob tail = 1/2
in your example consider an x a success and a y a failure
the probability of a success is 1/2
at this point you can apply the binomial if you are familiar
these problems become tricky if order matters, xyx vs xxy.
in any event, the outcome of the second flip does not depend on the first flip in any way. the same with the peppers, if you draw the green, replace it and draw again it is green or red, each with p = 1/2
 
Your husband is correct, it is more likely to get a mix of colours than two of the same color.
 
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