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

 
Maplesnowy  Feb 23, 2018

Best Answer 

 #1
avatar+26755 
+2

First calculate the probability, q, that no two dice show the same number:

 

first die:  any number

second die:  prob 5/6 that it is different from first

third die:      prob  4/6 that it is different from first two

fourth die:    prob  3/6 that it is different from first three

fifth die:       prob  2/6 that it is different from first four.

 

Hence;  q = 5*4*3*2/6^4

 

Porbability, p, that at least two show the same number is p = 1 - q

 

p = 1 - 5*4*3*2/6^4             (You can crunch the numbers!).

 
Alan  Feb 23, 2018
 #1
avatar+26755 
+2
Best Answer

First calculate the probability, q, that no two dice show the same number:

 

first die:  any number

second die:  prob 5/6 that it is different from first

third die:      prob  4/6 that it is different from first two

fourth die:    prob  3/6 that it is different from first three

fifth die:       prob  2/6 that it is different from first four.

 

Hence;  q = 5*4*3*2/6^4

 

Porbability, p, that at least two show the same number is p = 1 - q

 

p = 1 - 5*4*3*2/6^4             (You can crunch the numbers!).

 
Alan  Feb 23, 2018

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