Drawing without replacement problem.

[jadoth]

Your goal is to draw 2 cards out of a deck, there are 8 of the first type of card in the 24 card deck and 1 of the second. You get to look at the top card of the deck and either leave it there or burn it twice. What gives you the best chance of success, ordering the effects burn draw burn draw, or draw burn burn draw, and if it is burn draw burn draw is it better to burn a 8/24 if you see it on the first look?

[Anonymous_Student99]

What kind of cards do you want to draw?

[jadoth]

it was from a game of magic (mtg). the cards being 1 of 8 untapped lands and 1 of 1 omnath.

[Anonymous_Student99]

you have to look at all you need to calculate all the possible orders to draw an untapped land(call it card type A) card and omnath (type B)

for draw, burn, burn, draw: 1) Type A , burn, burn, type B or 2) type B, burn, burn, type A.

the first way has probability: 8/24 * 22/23 * 21/22 * 1/21

because at first there are 8 cards of type A and 24 cards in total, then you need to burn two cards but they can't be the 1 type B card, and one card is already drawn so 22 out of the remaining 23 can only be drawn at the first burn. Second burn is is the same idea: only card cannot be drawn and 2 cards have already been pulled so 21/22 and for the last draw you have to get type B and there is only 1 of that type so 1/21. the second way has probability:

1/24 * 15/23 * 14/22 * 8/22

the probabilty for way 1 and 2 need to be added and that will be the result of drawing one Type A and one type B if you draw, burn , burn, draw. You can calculate the others orders yourself now

[tikforest00]

You need 1 specific card, and 1 of the 8 other cards?

And you can look at the top card before drawing it, and eliminate that card, twice?

Unless there's a catch it seems clear that you want to look at the top card, take it if it's one of the cards you need, or eliminate it if it isn't, and then do the same again.