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October 9th, 2013, 05:56 PM  #1 
Newbie Joined: Oct 2013 Posts: 10 Thanks: 0  Complicated Card Probability
I basically have 6 cards to choose from Ace King Queen jack Ten Nine Pulling the Ace will give me $2 Pulling 2 picture cards will give me $3 Pulling the Ten AND nine will give me $5 I must pay the banker $1 to play a round. What is the chances of me winning at least $2?? And what is the chances of the banker keeping my $1??? Any help will be really appreciated. 
October 9th, 2013, 06:06 PM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,929 Thanks: 1124 Math Focus: Elementary mathematics and beyond  Re: Complicated Card Probability
Do you draw two cards per round? Do you draw cards with or without replacement?

October 9th, 2013, 06:33 PM  #3 
Newbie Joined: Oct 2013 Posts: 10 Thanks: 0  Re: Complicated Card Probability
yes draw 2 cards per round and draw the 2 cards at once. so without replacement i assume

October 9th, 2013, 07:04 PM  #4  
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53  Re: Complicated Card Probability Quote:
 
October 9th, 2013, 07:15 PM  #5 
Newbie Joined: Oct 2013 Posts: 10 Thanks: 0  Re: Complicated Card Probability
Okay so if I have a 1/3 chance of an Ace how about the rest? then how do i combine them together to work out my chances of getting at least $2?

October 9th, 2013, 07:25 PM  #6  
Senior Member Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53  Re: Complicated Card Probability Quote:
Quote:
 
October 9th, 2013, 07:47 PM  #7 
Newbie Joined: Oct 2013 Posts: 10 Thanks: 0  Re: Complicated Card Probability
So would I be right in saying 1/2 chance of picking a face card 1/6 chance of getting the ace and 2/6 of getting both the ten and nine. Would you be able to help me add them up? Because if I add them up it looks like a 100% chance to me? Not sure if I'm right though 
October 9th, 2013, 08:02 PM  #8 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,929 Thanks: 1124 Math Focus: Elementary mathematics and beyond  Re: Complicated Card Probability
Probability of picking an ace on the first draw: 1/6. Probability of picking an ace on the second draw: 5/6 * 1/5 = 1/6. Probability of picking an ace in a round: 1/6 + 1/6 = 1/3. Probability of picking a face card on the first draw: 1/2. Probability of picking a face card on the second draw (given a face card was picked on the first draw): 2/5. Probability of picking two face cards in a round: 1/2 * 2/5 = 1/5. Probability of picking either a nine or ten on the first draw: 1/3. Probability of picking the remaining card to make a 9, 10: 1/5. Probability of picking a nine and ten in a round: 1/3 * 1/5 = 1/15. In a round: Probability of winning a prize: 1/3 + 1/5 + 1/15 = 13/30. Probability the banker keeps your dollar (i.e. you win nothing): 1  13/30 = 17/30. Probability you make at least $2: 1/5 + 1/15 = 4/15. (You win either the three dollar prize or the five dollar prize). 
October 9th, 2013, 09:19 PM  #9 
Newbie Joined: Oct 2013 Posts: 10 Thanks: 0  Re: Complicated Card Probability
Thanks heaps for your help, I'll try keep going by my self from here on. appreciate it.


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