Card Game Probability Question

[Procrastinate]

In the card game Snap, two players each start with half of a shuffled deck. Alternately, each player turns up the top card of their pile. When the top cards of the face-up piles match (but are obviously different suits), the first person to say “snap” gets both face-up piles. When a player reaches the bottom of their pile, both players shuffle their cards then resume playing.

b. What is the probability that the players will turn over 4 cards (2 each without a match).

P(turn over 4 cards with no match: 48/51 * 44/50 * 40/49 * 36/48 = 2112/4165

Unfortunately, that was the wrong answer. The answer is 3464/4165 and I am not sure why.

 

[tiny-tim]

Hi Procrastinate!

b. What is the probability that the players will turn over 4 cards (2 each without a match).

P(turn over 4 cards with no match: 48/51 * 44/50 * 40/49 * 36/48 = 2112/4165

He he … you've obviously never played snap!

You can only shout "SNAP!" if the top cards on each pile match.

 

[Tedjn]

You are calculating when all 4 cards are different. But that's not the only way for no matches to occur.

 

[Procrastinate]

You are calculating when all 4 cards are different. But that's not the only way for no matches to occur.

Actually, my mistake, I forgot to add the previous cards back in since they are no longer the top card. Therefore it is:

48/51*47/50*46/49

 

[Tedjn]

You are still missing a case. What happens if the third card is equal to the first card?