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10 Feb 2006, 13:41
Kudos
Bookmarks
suppose we have two players that successively draw a card from a standard 52 cards deck, they start the game with 5 dollars each. Each time they play if they observe a red card they make $1, if they observe a black card they have to pay $1.
The game ends when one of the players has no money remaining.(goes bankrupt)
what is the probability that the players can play 5 times before a player bankrupts?
The game ends when one of the players has no money remaining.(goes bankrupt)
what is the probability that the players can play 5 times before a player bankrupts?
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10 Feb 2006, 20:34
Kudos
Bookmarks
Will this kind of question be on the test? I need to use a calculator for this one... correct if wrong.
Assume Player 1 draws first.
In order to bankrupt before both players play 5 times, one player has to get Black cards 5 times in a roll. BBBBB = 0 dollars.
Player 1 and 2
52 50 48 46 44 = 252595200
26 24 22 20 18 BBBB = 4942080
26 24 22 20 19 BBBR = 5216640
26 24 22 21 19 BBRB = 5477472
26 24 23 21 19 BRBB = 5726448
26 25 23 21 19 RBBB = 5965050
26 24 22 21 20 BBRR = 5765760
26 24 23 22 20 BRRB = 6314880
26 25 24 22 20 RRBB = 6864000
26 25 23 22 20 RBRB = 6878000
26 24 23 21 20 BRBR = 6027840
26 25 23 21 20 RBBR = 6279000
26 24 23 22 21 BRRR = 6630624
26 25 23 22 21 RBRR = 6906900
26 25 24 22 21 RRBR = 7207200
26 25 24 23 21 RRRB = 7534800
26 25 24 23 22 RRRR = 7893600
1 - (101630294/252595200) = 59.765548197273740752001621566839%
Assume Player 1 draws first.
In order to bankrupt before both players play 5 times, one player has to get Black cards 5 times in a roll. BBBBB = 0 dollars.
Player 1 and 2
52 50 48 46 44 = 252595200
26 24 22 20 18 BBBB = 4942080
26 24 22 20 19 BBBR = 5216640
26 24 22 21 19 BBRB = 5477472
26 24 23 21 19 BRBB = 5726448
26 25 23 21 19 RBBB = 5965050
26 24 22 21 20 BBRR = 5765760
26 24 23 22 20 BRRB = 6314880
26 25 24 22 20 RRBB = 6864000
26 25 23 22 20 RBRB = 6878000
26 24 23 21 20 BRBR = 6027840
26 25 23 21 20 RBBR = 6279000
26 24 23 22 21 BRRR = 6630624
26 25 23 22 21 RBRR = 6906900
26 25 24 22 21 RRBR = 7207200
26 25 24 23 21 RRRB = 7534800
26 25 24 23 22 RRRR = 7893600
1 - (101630294/252595200) = 59.765548197273740752001621566839%
10 Feb 2006, 22:39
Kudos
Bookmarks
well , yesterday a friend of mine helped me with this problem.
prob of getting a black card = 26/52 =1/2
prob of getting a red vard = 26/52 = 1/2
losing all the 5$ - going bankrupt means getting red all the time
therefore 1/2*1/2*1/2*1/2*1/2= 1/32
OA please. This is a damm good question.
prob of getting a black card = 26/52 =1/2
prob of getting a red vard = 26/52 = 1/2
losing all the 5$ - going bankrupt means getting red all the time
therefore 1/2*1/2*1/2*1/2*1/2= 1/32
OA please. This is a damm good question.
