>>10680437>In your dice example, the chance of rolling an even number is far greater than rolling an odd number, even if specifically chosing an even number has the same chance of rolling that one odd number.That's exatcly right!
It IS true that the chance of rolling an even number is far greater than rolling an odd number.
It IS NOT true that picking an even number gives you a higher probability of winning than picking an odd number.
So you agree with this statement right?:
"In the game where a dice with the numbers 2, 4, 6, 8, 10 and 11 will be rolled, and you have to give one number as your prediction,
then choosing an even number (aka choosing a number from the set {2,4,6,8,10}) will not give you a higher probability of winning than choosing an odd number (aka choosing a number from the set {11}). "
If you agree with that, then equivalently you should agree with:
"In a lottery where 5 numbers are randomly picked from {1,...,90}, and you have to give 5 numbers as your prediction,
then choosing 5 even numbers (aka choosing 5 numbers from the set {2,4,...,88,90}) will not give you a higher probability of winning than choosing 5 prime numbers (aka choosing a number from the set {2,3,5,7,11...}). "
>>10680494thanks, you do a better job of explaining it than me