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Define the term "equivalent events". If $M$ is the event that the number rolled from a die is a prime number, which event can be equivalent to $M$?

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Unless you can give us some context even to understand what is meant by "equivalent events," Georgia, we will need to close this as an incomprehensible question. – whuber♦ Aug 16 '12 at 15:20

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The possible outcomes for the roll are $\{1, 2, 3, 4, 5, 6\}$. The primes in this set are $\{2, 3, 5\}$, so the event $M$ is in a single roll of a die a 2, 3, or 5 is rolled. I haven't seen a definition of "equivalent event", but if I were to hazard a guess, I would say that 2 events are "equivalent" if they have the same probability distribution. Since $M$ has a 50:50 probability distribution (assuming a fair die), it is equivalent to a coin flip.

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Since 2, 3 and 5 are the primes in the set of integers from 1 to 6, rolling a 2 or 3 or a 5 is equivalent to rolling a prime.

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I understand an 'event' to be a measurable set, but obviously you cannot be asserting that $\{2,3,5\}$ is the same as $\{3\}$ or $\{5\}$, or even has the same probability. What, then, do you mean by equivalent? (The question probably comes down to the definition of "equivalent." I would argue that the question is ill-posed and cannot be answered as is because "equivalent" has so many common definitions.) – whuber♦ Aug 15 '12 at 20:24
so how do we define 'equivalent events'? – Georgia Markadji Aug 15 '12 at 20:26
I am taking equivalent to me different ways of expressing identical events. So in the example occurrence of a prime is the same as saying a 3 or a 5 occurs. We have a very simple discrete probability measure here. A roll of the die will yield 1 or 2 or 3 or 4 or 5 or 6 with probabilities p$_1$ to P$_6$ summing to 1 and usually assuming a balanced die p$_i$ equals 1/6 for each i. – Michael Chernick Aug 15 '12 at 20:32
2 is prime. I agree that rolling a 3 is equivalent to rolling a 5 in this event space, but I don't think rolling a 3 is equivalent to $M$, because $M$ is 2 or 3 or 5. – shujaa Aug 15 '12 at 22:11
Sorry I forgot about the only even prime! I edited my answer accordingly. – Michael Chernick Aug 15 '12 at 22:14

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