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?

Guest Jan 19, 2022

#1**0 **

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.

ImDecentAtMath Jan 19, 2022

#2**0 **

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.

Guest Jan 19, 2022

#3**0 **

*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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Guest Jan 20, 2022