Suppose the sample space of an experiment is the set of prime numbers. Is it possible...

Suppose the sample space of an experiment is the set of prime numbers. Is it possible for all outcomes to be equally likely? Why? Is it possible for all outcomes to have nonzero probability? Explain.

Expert Solution

The Sample smpace here is set of prime numbers which is {2,3,5,7,11,......}

All the outcomes are equally likley if the probability of all the outcomes is same

Lets say there are N prime nunbers

Probability of outcome 2 = 1/N

Probability of outcome 3 = 1/N

Probability of outcome 5 = 1/N

Likwise the probability of each outcome here is 1/N

Sum of the probabilities of all the outcomes is 1

So all the outcomes are equally likely

All the outcomes will have a probability of 1/N if there are total N prime numbers.

So all the outcomes will have a probability of 1/N which is non-zero

In short, All the outcomes are equally likely and probability of each outcome is non-zero

orchestra answered 2 years ago

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