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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 19, 2022
 #1
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This I think should be simple. I hope I'm not getting too overconfident but I think it's just (3/6)*(2/5)*(1/4)=1/20.

So the chance of everyone getting a red card is 1/20.

 Jan 19, 2022
 #2
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There are six cards going to three people, so everybody gets two cards. 

 

There's only one way that not everybody gets a red card,  

and that way is if one person gets two yellow cards. 

And only one person could get two yellow cards.  

 Jan 19, 2022
 #3
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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?

 

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%.  

.

 Jan 20, 2022

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