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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

Mathematics
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The whole roll 2n+1 times, get k even numbered die is a binomial distribution but I wonder
if the symmetry of the probability can't make this a bit easier.
We can definitely use the fact that it is multiple choice though...

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Other answers:

If \(n=0\) then clearly getting an even face means you win, so the probability is \(1/2\).
Which knocks out b and c
i am getting d as the answer , but the book is saying a.
When \(n=1\). what is the probability?
You have three rolls, if you roll 1 or 3 evens, you win
hm,yes
oops, that doesn't actually matter, when \(n=1\) then a) is still 1/2
They need to be different.
n=2 gives 7/10 for a, but d is still 1/2 so.... 5 rolls, what is the probability of odd even rolls
Weird... There is no explanation for a)?
D i think

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