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Probability and Permutations and Combinations

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Probability and Permutations and Combinations

by bhumika.k.shah » Wed Jan 27, 2010 9:24 am
Three cards are drawn at random from a standard deck of playing cards
without replacement. What is the probability that:

a) all 3 cards are Aces?
b) at least one of the cards is a picture card?
c) there is at most one heart?
d) each card has a different face value?

Detailed Explanations pleaseeee :-)
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by thephoenix » Wed Jan 27, 2010 9:32 am
bhumika.k.shah wrote:Three cards are drawn at random from a standard deck of playing cards
without replacement. What is the probability that:

a) all 3 cards are Aces?

4C1*3C1*2C1/52C1*51C1*50C1=24/52*51*50
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by bhumika.k.shah » Wed Jan 27, 2010 9:36 am
?
thephoenix wrote:
bhumika.k.shah wrote:Three cards are drawn at random from a standard deck of playing cards
without replacement. What is the probability that:

a) all 3 cards are Aces?

4C1*3C1*2C1/52C1*51C1*50C1=24/52*51*50

b) at least one of the cards is a picture card?
1-40C1/52C1=8/52


Detailed Explanations pleaseeee :-)
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by thephoenix » Wed Jan 27, 2010 9:40 am
bhumika.k.shah wrote:Three cards are drawn at random from a standard deck of playing cards
without replacement. What is the probability that:


b) at least one of the cards is a picture card?

Detailed Explanations pleaseeee :-)
1-NONE IS PIC CARD
1-[(40C1/52C1)*(39C1/51C1)*(38C1/50C1)]
Last edited by thephoenix on Wed Jan 27, 2010 9:49 am, edited 1 time in total.
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by ajith » Wed Jan 27, 2010 9:41 am
bhumika.k.shah wrote:Three cards are drawn at random from a standard deck of playing cards
without replacement. What is the probability that:

a) all 3 cards are Aces?
b) at least one of the cards is a picture card?
c) there is at most one heart?
d) each card has a different face value?

Detailed Explanations pleaseeee :-)
a) 4/52*3/51*2/50 (4 aces in a deck)

b) At least one Picture card can be subdivided into

1. Exactly 1 picture card 2. Exactly 2 Picture cards 3. Exactly 3 Picture cards

exactly one is picture + exactly two are picture + exactly 3 are picture
12/52*40/51*39/50+ 12/52*11/51*40/50+ 12/52*11/51*10/50


c) exactly 0 heart + exactly 1 heart
39/52*38/51*37/50 + 13/52*39/51*38/50

d) d) 1*48/51*44/50
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by thephoenix » Wed Jan 27, 2010 9:45 am
bhumika.k.shah wrote: FOR d
52C1*48*C1*44C1=52*48*44
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by ajith » Wed Jan 27, 2010 9:48 am
thephoenix wrote:
bhumika.k.shah wrote: FOR d
52C1*48*C1*44C1=52*48*44
The question asks the probability, ThePhoenix :)
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by thephoenix » Wed Jan 27, 2010 9:54 am
ajith wrote:
thephoenix wrote:
bhumika.k.shah wrote: FOR d
52C1*48*C1*44C1=52*48*44
The question asks the probability, ThePhoenix :)
YEAH THANKS
IT WILL BE 52/52 * 48/51 *44/50

THANKS FOR WAKING ME
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by bhumika.k.shah » Wed Jan 27, 2010 9:56 am
Is it the same as 4C3 / 52C3????
ajith wrote:
bhumika.k.shah wrote:Three cards are drawn at random from a standard deck of playing cards
without replacement. What is the probability that:

a) all 3 cards are Aces?


a) 4/52*3/51*2/50 (4 aces in a deck)
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by ajith » Wed Jan 27, 2010 9:59 am
bhumika.k.shah wrote:Is it the same as 4C3 / 52C3????
ajith wrote:
bhumika.k.shah wrote:Three cards are drawn at random from a standard deck of playing cards
without replacement. What is the probability that:

a) all 3 cards are Aces?


a) 4/52*3/51*2/50 (4 aces in a deck)

Yup it is the same as 4C3/52C3
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by bhumika.k.shah » Wed Jan 27, 2010 7:01 pm
Hey ajith could you explain all of these in the PnC formula way???

Like i know for a.) the answer is 4C3/52C3

Thanks!
:)
ajith wrote:
bhumika.k.shah wrote:Three cards are drawn at random from a standard deck of playing cards
without replacement. What is the probability that:

a) all 3 cards are Aces?
b) at least one of the cards is a picture card?
c) there is at most one heart?
d) each card has a different face value?

Detailed Explanations pleaseeee :-)
a) 4/52*3/51*2/50 (4 aces in a deck)

b) At least one Picture card can be subdivided into

1. Exactly 1 picture card 2. Exactly 2 Picture cards 3. Exactly 3 Picture cards

exactly one is picture + exactly two are picture + exactly 3 are picture
12/52*40/51*39/50+ 12/52*11/51*40/50+ 12/52*11/51*10/50


c) exactly 0 heart + exactly 1 heart
39/52*38/51*37/50 + 13/52*39/51*38/50

d) d) 1*48/51*44/50
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