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

 Feb 5, 2022
 #1
avatar+69 
+4

We can use complementary counting, which is, subtracting the possibilities that don't satisfy the condition from the total amount of possibilities.

 

For the first die, the probability that two dice don't show the same number is 1. 

For the second die, the probability is 5/6, because one possibility was taken from the first die. 

For the third die, the probability is 4/6 or 2/3 because two possibilities have been taken from the two dice already rolled. 

Therefore, we see that the fourth and fifth have 3/6 (1/2) and 2/6 (1/3) as their probability. 

 

We multiply these all together and we get

 

1 * 5/6 * 2/3 * 1/2 * 1/3 = 5/54.

 

⚡⚡⚡

ShockFish

 

(This question was also answered here: https://web2.0calc.com/questions/help-one-more-problem)

 Feb 5, 2022
 #2
avatar+117861 
+1

thanks Shockfish,

I alwasy like playing with these, I hope you don't mind.

 

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

 

What is the prob that they are all different

1*5/6*4/6*3/6*2/6 = 5! / 6^4 = 120 / 1296 = 5/54

 

So the prob that they are NOT all different is     1 - 5/54  =    49/54

 Feb 5, 2022

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