My Math Forum Complicated Card Probability

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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
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Re: Complicated Card Probability

Quote:
 Originally Posted by Rollsroyce 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.
You can find each of the probabilities by making a tree diagram. For example, in the first question, you can either draw an ace on your first draw which has 1/6 chance of happening, or you can not draw an ace on your first draw and draw it on your second one, which has (5/6)(1/5)=1/6 chance of happening, so the total probability of drawing and ace is (1/6)+(1/6)=1/3.

 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:  Originally Posted by Rollsroyce 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?
You can't figure it out yourself after I just showed you? I'll get you started: There's a 1/2 chance of picking a face card on the first draw, and a 1/2 chance of not picking one on the first draw.

Quote:
 Originally Posted by Rollsroyce how do i combine them together to work out my chances of getting at least $2? If you get at least$2, that must mean that you won one of prizes previously stated. So just add up all the probabilities...

 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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