Question

Christina calculated the probability of choosing an even number from a list of test grades to be . What is the probability of choosing an odd number?

Answer 1

Answer:

It depends on what probability distribution one defines on N (as observed, this cannot be a uniform distribution, but that doesn't mean no distribution exists). Consider the following probability assignments on N:

Prob(1) = 1/2, Prob(2) = 1/4, ..., Prob(n) = 1/2n [this is a legitimate probability distribution since the sum of all terms is 1]

Here obviously the probability of picking an even number is 1/4 + 1/16 + ..., which is 1/3, not 1/2. On the other hand, we could 'split the distribution in two' thus:

Prob(1) = prob(2) = 1/4, Prob(3) = Prob(4) = 1/8, ..., Prob(2k−1) = Prob(2k) = 1/4k

Here obviously the probability of picking an even number is 1/2 since the odd and even terms must separatlon.