Furthermore, the tries must be independent of each other, otherwise the reasoning breaks down completely. If I draw cards from a deck, each one has (a priori) 1⁄52 chance of being the ace of spades, yet if I draw all 52 I will draw the ace of spades 100% of the time. This is because successive failures increase the posterior probability of drawing a success.
Furthermore, the tries must be independent of each other, otherwise the reasoning breaks down completely. If I draw cards from a deck, each one has (a priori) 1⁄52 chance of being the ace of spades, yet if I draw all 52 I will draw the ace of spades 100% of the time. This is because successive failures increase the posterior probability of drawing a success.
Yes! That’s a good point that I didn’t mention.