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Each of five, standard, six-sided dice is rolled once. What is the probability that there is at least one pair among all five rolls?  (In other words, what is the probability that at least two rolls are equal?)

Nov 21, 2020

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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  = 1 - (120 / 6^4) =0.9074 x 100 =90.74%

Nov 21, 2020

#1
0

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  = 1 - (120 / 6^4) =0.9074 x 100 =90.74%

Guest Nov 21, 2020