Math Is Fun Forum

Heron

Guest

Probability Question

Hey guys,
This website seems like it has an amazing community, so I thought you might be able to help me. I am doing homework for my math class, but this one probability question keeps stumping me!

"Jan has a stack of 8 cards consisting of J,J,J,J,Q,Q,Q,Q. Jan shuffles the stack then deals out the top 3 cards. What is the probability that two of the cards dealt were Jacks and one was a Queen?"   

I keep calculating

. However, the answer is

. Could someone show me how to derive this answer?

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Probability Question

Hej Heron,

What you have calculated is probability of getting JJQ, in that order. You also have JQJ and QJJ, which have the same probabilities as JJQ, so it's just 3*1/7=3/7.

Last edited by anonimnystefy (2015-02-25 12:55:43)

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability Question

Hi;

These are the 8 possibilities...

{{j, j, j}, {j, j, q}, {j, q, j}, {j, q, q}, {q, j, j}, {q, j, q}, {q,q, j}, {q, q, q}}

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

anonimnystefy

Real Member

From: Harlan's World

Registered: 2011-05-23

Posts: 16,049

Re: Probability Question

What is the probability that two of the cards dealt were Jacks and one was a Queen?

He wants exactly two Jacks and one Queen to be dealt.

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“Here lies the reader who will never open this book. He is forever dead.
“Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment
The knowledge of some things as a function of age is a delta function.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability Question

Hi;

I know that, I am saying should it not be 3/8 instead of 3/7?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,643

Re: Probability Question

hi Heron,

Welcome to the forum.

This is my explanation.

P(JJQ) = 4/8 x 3/7 x 4/6

P(JQJ) = 4/8 x 4/7 x 3/6

P(QJJ) = 4/8 x 4/7 x 3/6

This P(JJQ in any order+ = 3 x 4/8 x 4/7 x 3/6 = 3/7

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Probability Question

Hi Bobbym;

I know that, I am saying should it not be 3/8 instead of 3/7?

A curious oversight. Aren't you claiming that each of those 8 possibilities are equally likely?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability Question

Hi;

A curious oversight. Aren't you claiming that each of those 8 possibilities are equally likely?

That gator must have landed one too many blows to my melon. You are correct, Bob's analysis is the right way, I am sorry all.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

ElainaVW

Member

Registered: 2013-04-29

Posts: 580

Re: Probability Question

See you in Florida after I get back.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Probability Question

When will that be? Have you seen the rational term problem on the other forum?

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.