SOLUTION: Sandy and Claude are playing a game in which there are 5 tiles in a bag, numbered 1 through 5. The game is played by the players taking turns pulling out a tile without replacing i

Question 394723: Sandy and Claude are playing a game in which there are 5 tiles in a bag, numbered 1 through 5. The game is played by the players taking turns pulling out a tile without replacing it. A player wins if they pull out the tile numbered "3". If Sandy goes first, what is the probability that she will win?
choose the answer and explain the reason to choose your response
50%
45%
75%
60%
Answer by jrfrunner(365) (Show Source): You can put this solution on YOUR website!
p(sandy wins/she goes first)=0.6
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reasoning
on her first try, she has 1/5 chance of getting the "3" tile and wins
if she does not get the "3" tile, then clause has 3/4 of not getting the "3" tile since there are only 4 tles left and the game can continue.
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On Sandy's second try, there are only 3 tiles left and for Sandy to get a second chance to win, she must of failed the first time 4/5 chance and Claude must of failed 3/4 chance and for Sandy to win in the second try she has 1/3 chance so Sandy can win on the second try with 4/5*3/4*1/3=1/5
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If Sandy does not win of the second, she gets a third try if she failed on the first and Claude failed oh his first and sandy failed on her second and cluade failed on his second and finally Sandy tries a 3rd time. This can happen by Sandy failing on first 4/5 chance, Claude failing first 3/4 chance, sandy failing on second 2/3 chance and claude failing on his second with 1/2 chance
or 4/5*3/4*2/3*1/2=1/5
after this there are no more tiles
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So sandy wins by going first if she wins on the first try, or second try or 3rd try = 1/5+1/5+1/5=3/5=0.6

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