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Consider a dice with the property that the probability of a face with $n$ dots showing up is proportional to $n$. The probability of the face with three dots showing up is ________.
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X 1 2 3 4 5 6
P(X) k 2k 3k 4k 5k 6k

where, k is a proportional constant.

∑P(X)=1

k+2k+3k+4k+5k+6k = 1

k= 1/21

P(3 dots) = 3* 1/21 =3/21 (Answer)

by (140 points)
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Why we are equating it to 1
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Because summation of any random event is always equal to 1 in probability

Probability of having an event+ probability of not having an event =1

p+ ~p = 1
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