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Jack rolls 5 fair six-sided dice. What is the probability that at least three dice show the same number? 

 Nov 1, 2020

Best Answer 

 #2
avatar+111600 
+1

6^5 =7776 possible outcomes (order counts)

 

N,A and B represent different numbers that can be thrown

 

 

NNNNN       6 ways

NNNNA       6*5*5 =150ways

NNNAA       6*5*5C2=30*10 = 300 ways

NNNAB       6*5*4 *5C2= 120*10= 1200 ways

1200+300+150+6 = 1656  (order counts)

 

P(at least 3 the same) =   1656/7776 = 23/108

 

 

 

I do not guarantee my answers, especially not counting and probability answers.

This answer does seem higher than I would have expected.

 Nov 1, 2020
 #1
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+1

(5 nCr 3 * 5^2) + (5 nCr 4 * 5^1) + (5 nCr 5 * 5^0) = 276 / 6^5 =23 /648

[Sorry Melody. Didn't know you were working on it]

 Nov 1, 2020
 #4
avatar+111600 
0

You did not need to appologize :)

Could you elaborate on your answer please.

Melody  Nov 1, 2020
 #5
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Sorry, you got it spot on. It is: 1656 / 7776 =23 / 108. I just verified it by a computer code. The first stupid answer I worked out was for "at least 3 specific numbers, such as 3 ones"

Guest Nov 1, 2020
 #6
avatar+111600 
0

Thanks   cool

What coding language did you use?

One of these days I will learn to code in some modern language.   

Melody  Nov 1, 2020
 #8
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+1

C++.

Guest Nov 2, 2020
 #9
avatar+111600 
0

Thank you.

That sounds like a commonly used one.

I think some people use Python.

I guess when I am ready to learn I will work out the best one for me.

(probably the easiest one that I can download for free)

Melody  Nov 2, 2020
 #2
avatar+111600 
+1
Best Answer

6^5 =7776 possible outcomes (order counts)

 

N,A and B represent different numbers that can be thrown

 

 

NNNNN       6 ways

NNNNA       6*5*5 =150ways

NNNAA       6*5*5C2=30*10 = 300 ways

NNNAB       6*5*4 *5C2= 120*10= 1200 ways

1200+300+150+6 = 1656  (order counts)

 

P(at least 3 the same) =   1656/7776 = 23/108

 

 

 

I do not guarantee my answers, especially not counting and probability answers.

This answer does seem higher than I would have expected.

Melody Nov 1, 2020
 #7
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0

xxxxxxxxxx

 Nov 1, 2020
edited by Guest  Nov 1, 2020

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