sritama
A fair die is rolled (2n+1) times.The probability that the faces with even number show odd number of times is
a) (3n+1)/(4n+2) b) 3/4
c)2/3 d)1/2



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wio
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The whole roll 2n+1 times, get k even numbered die is a binomial distribution but I wonder

wio
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if the symmetry of the probability can't make this a bit easier.

wio
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We can definitely use the fact that it is multiple choice though...

wio
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If \(n=0\) then clearly getting an even face means you win, so the probability is \(1/2\).

wio
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Which knocks out b and c

sritama
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i am getting d as the answer , but the book is saying a.

wio
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When \(n=1\). what is the probability?

wio
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You have three rolls, if you roll 1 or 3 evens, you win

sritama
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hm,yes

wio
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oops, that doesn't actually matter, when \(n=1\) then a) is still 1/2

wio
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They need to be different.

wio
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n=2 gives 7/10 for a, but d is still 1/2 so....
5 rolls, what is the probability of odd even rolls

wio
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Weird...
There is no explanation for a)?

timo86m
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D i think