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?)

Guest 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

#1**0 **

Best Answer

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