Originally Posted by
Jabba
Humots,
- This is going to take me awhile, but so far, I can't figure out why we can't just compare the 2 "combined" probabilities -- i.e. combined probability #1) the probability of randomly selecting the ace deck from the total number of decks (.02), times the probability of drawing an ace, once the ace deck has been chosen (1.00), and #2) the probability of randomly selecting a normal deck from the total number of decks (.98), times the probability of drawing an ace, once the normal deck has been chosen (.076923077).
- Consequently, before we get started, the probability of chosing the ace deck and then drawing an ace is .02*1.00, or .02, while the probability of chosing a normal deck and then drawing an ace is .98*.076923077, or .075384615. And, the probability of drawing an ace via the second route is almost 4 times as large as the probability of doing it via the first.
--- Jabba
- The smilie at the top is an accident, but I don't know how to get rid of it.
Because as I understand it, the question is not:
What is the probability that we select the All-Ace deck and draw an Ace?
vs
What is the probability that we select the regular deck and draw an Ace?
It is:
If we draw a card from a deck (and we don't know which one) and the card is an Ace, what is the probability that we drew from the All-Ace deck?
The point is, there are not two separate events, each with its own probability. There is only one event: drawing a card from a deck and the card is an ace.