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There is a very simple rule when it comes to probability. It all has to add up. If you have two choices, it's simply not possible to have 2 different odds.
1 in 2 = 0.5
1 in 3 = 0.3 recurring.
Add them up and you have 0.83 recurring. It needs to add up to 1. Or else 17 percent of the time, you'd be having no result, and that's simply not possible. How do you account for the remaining 17 percent? Or am i missing something here?
I mean, 1 in 2 is the same as 3 in 6. And 1 in 3 is the same as 2 in 6. So what about the remaining 1 in 6? What is the probability that it'll be the prize or won't be the prize?
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26 + 6 = 1
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