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

Maplesnowy
Feb 23, 2018

#1**+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**+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