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# Help, one more problem

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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

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+26547
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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
Sort:

#1
+26547
+1

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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