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# Probability question

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The following cards are dealt to three people at random, so that everyone gets the same number of cards.  What is the probability that everyone gets a red card?

Jan 20, 2022

#1
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Well, it's (3/6)*(2/5)*(1/4)=1/20.

So the chance is 1/20.

Jan 20, 2022
#2
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I have to disagree.  Here's a copy of the answer I gave the first time I saw this problem:

The following cards are dealt to three people at random, so that everyone gets the same number of cards. What is the probability that everyone gets a red card?

These are the possible hands that could be dealt.

REDA REDB    REDA REDC    REDA YELA    REDA YELB    REDA YELC

REDB REDC    REDB YELA    REDB YELB    REDB YELC

REDC YELA    REDC YELB    REDC YELC

YELA YELB     YELA YELC

YELB YELC

As you can see, there are fifteeen possible hands that could be dealt.

Twelve of those hands have at least one red card.

So the likelihood of receiving at least one red card is 12/15 which reduces to 4/5 or 80%.

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Jan 21, 2022
#4
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I do not understand what you have done guest.  There are 3 people and 6 cards so they get 2 cards each.

Why do you have 2 lots of 4?

Melody  Jan 21, 2022
#5
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Hi Melody.

Yes, each player gets two cards. I don't know what you mean by 2 lots of 4.

REDA REDB is one hand of two cards.  The red A card and the red B card.

Another example is REDB YELB.  The red B card and the yellow B card.

I illustrated 15 hands of 2 cards each.  Would it have been clearer if I had used

a hyphen or a virgule between the two cards in each hand?  Like REDA-YELC?

Red A Red B is the same as Red B Red A so I omitted the latter, and so on.

You said 6 cards ordered 6! ways.  I don't see it that way.

I see it as 6C2, or a combination of 6 items taken 2 at a time.

Ron

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Guest Jan 21, 2022
#6
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I still don't know what you are talking about.

"REDA REDB is one hand of two cards. "

How is this one hand of two cards.  There are 2 lots of 4 letters here.  It makes no sense.

Thanks for responsing though.  I gave you are point just for responding.

Melody  Jan 21, 2022
edited by Melody  Jan 21, 2022
edited by Melody  Jan 21, 2022
#7
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MELODY

Please don't give up on me yet.  The light came on over my head.  I know what you mean now.

You're looking at REDA REDB as "There are 2 lots of 4 letters here

referring to the four individual letters.  My answer wasn't clear enough.

for example, REDA means the red A card ... the A card

YELA means the yellow A card ... the A card (yellow didn't show up, I had to use gold)

So REDA REDB means two cards:  A and B

Would it have been more clear if I had called them Ared and Bred?  Or RedA and RedB?

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Guest Jan 22, 2022
#3
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6 cards can be ordered in 6! ways

but ABCDEF  is the same as BACDEF etc

6! / 2^3=  90 ways to distribute the cards.

3!*3! ways for them to get a read each  = 36 ways

36/90 = 40%

Jan 21, 2022