Probability Question
March 5th, 2011 at 7:16:15 AM
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Im trying to figure out as to how to solve this, any help is appreciated XD:
Q1)A player draws two cards from a deck of 52 cards. The player then draws a third card (without replacement), the player wins if the third card is between the first two cards drawn. What is the probability tha the player will win if he/she plays the game?
Q2) Same as the first question, but instead of drawing only a third card, he draws two more cards(without replacement). The player wins if the two cards are between the first two drawn cards. Whats the probability of winning now?
Q1)A player draws two cards from a deck of 52 cards. The player then draws a third card (without replacement), the player wins if the third card is between the first two cards drawn. What is the probability tha the player will win if he/she plays the game?
Q2) Same as the first question, but instead of drawing only a third card, he draws two more cards(without replacement). The player wins if the two cards are between the first two drawn cards. Whats the probability of winning now?
March 5th, 2011 at 7:29:09 AM
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How are you counting Aces? Always high, always low, whatever gives the biggest spread, whatever gives the smallest spread, or something else?
“Man Babes” #AxelFabulous
March 5th, 2011 at 7:33:08 AM
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Counting Aces as 1 and J,Q,K as 10
March 5th, 2011 at 8:07:55 AM
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I get 22.009049773756 % for 1 card and 8.6286822421276 % for 2 cards. So, are you the take a fish kind of person, or a fishing pole type?
“Man Babes” #AxelFabulous
March 5th, 2011 at 8:32:14 AM
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Fishing Pole lol, can you tell me how you went about in getting the awnser please
March 5th, 2011 at 9:07:30 AM
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There are combin(52,2)= 1326 different 2 card starting combinations.
Next figure out how many have a spread of 1 ( 1 3, 2 4, 3 5, 4 6, 5 7, 6 8, 7, 9, 8 10). The first 7 pairs have 16 ways each, (four 3's and four 5's) . 8 10 has 4*16=64 ways. 64 + 16*7 = 176. There are then 50 cards left to choose from and 4 will be in the middle. (176/1326)*(4/50)=0.010618401206636.
Spread of 2 (1 4, 2 5, 3 6, 4 7, 5 8, 6 9, 7 10). First 6 pairs have 16 ways. 7 10 has 64. 6*16 + 64 = 160. Of the 50 cards left, 8 will be in the middle. (160/1326)*(8/50)= 0.019306184012066
Keep on until spread of 8 (1 10) 64 ways, 32 in the middle (64/1326)*(32/50)= 0.030889894419306
Add all the final numbers up to get 0.22009049773756 .
....
To do the 2 card ones you'll use a different fraction. There are combin(50,2)=1225 total possible 2 cards to draw. For 1 card spread there are combin(4,2)=6 combinations of cards that will be in the middle. (176/1326)*(6/1225)=0.000650106196325
Spread of 2 = combin(8,2)=28 combinations of cards that will be in the middle. (160/1326)*(28/1225)=0.002758026287438
ect...
Add all the final numbers up to get 0.086286822421276 .
Hope that helps. Any questions, just ask.
Next figure out how many have a spread of 1 ( 1 3, 2 4, 3 5, 4 6, 5 7, 6 8, 7, 9, 8 10). The first 7 pairs have 16 ways each, (four 3's and four 5's) . 8 10 has 4*16=64 ways. 64 + 16*7 = 176. There are then 50 cards left to choose from and 4 will be in the middle. (176/1326)*(4/50)=0.010618401206636.
Spread of 2 (1 4, 2 5, 3 6, 4 7, 5 8, 6 9, 7 10). First 6 pairs have 16 ways. 7 10 has 64. 6*16 + 64 = 160. Of the 50 cards left, 8 will be in the middle. (160/1326)*(8/50)= 0.019306184012066
Keep on until spread of 8 (1 10) 64 ways, 32 in the middle (64/1326)*(32/50)= 0.030889894419306
Add all the final numbers up to get 0.22009049773756 .
....
To do the 2 card ones you'll use a different fraction. There are combin(50,2)=1225 total possible 2 cards to draw. For 1 card spread there are combin(4,2)=6 combinations of cards that will be in the middle. (176/1326)*(6/1225)=0.000650106196325
Spread of 2 = combin(8,2)=28 combinations of cards that will be in the middle. (160/1326)*(28/1225)=0.002758026287438
ect...
Add all the final numbers up to get 0.086286822421276 .
Hope that helps. Any questions, just ask.
“Man Babes” #AxelFabulous
