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Question

To play a game, a die is rolled to see who plays first. Four players are going to play the game. What is the probability that at least two people roll the same number? Express your answer to the nearest tenth of one percent.

Answer 1

This is 1 minus the probability that all four numbers are different.

There are 6 * 6 * 6 * 6 = 6^4 ways for the four players to each roll a die. Player A has 6 possibilities, Player B also, etc. and the roll is independent for all 4 players. So, 6^4 = 1296.

How many ways are there for the four players to roll different numbers? Player A has 6 possibilities. Player B now has only 5, because s/he can't roll the same number that A rolled. Player C has only 4, and Player D has only 3. So there are 6*5*4*3 = 360 ways this can be done. This corresponds to the number of ordered combinations n! / (n-k)! where n=6 and k=4.

So the probability of no two numbers being the same is 360 / 1296 = 5/18. The probability of having at least two identical numbers is therefore 13/18 = 72.2%.

Answer 2

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I can't help u
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