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October 9th, 2013, 05:56 PM   #1
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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.
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October 9th, 2013, 06:06 PM   #2
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Re: Complicated Card Probability

Do you draw two cards per round? Do you draw cards with or without replacement?
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October 9th, 2013, 06:33 PM   #3
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Re: Complicated Card Probability

yes draw 2 cards per round and draw the 2 cards at once. so without replacement i assume
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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.
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October 9th, 2013, 07:15 PM   #5
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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?
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October 9th, 2013, 07:25 PM   #6
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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...
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October 9th, 2013, 07:47 PM   #7
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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
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October 9th, 2013, 08:02 PM   #8
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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).
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October 9th, 2013, 09:19 PM   #9
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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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