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