if there are 5 people in a room and each chooses a number from 1 to 10 at random what is the probability that two or more people have the same number

First work out the probability that none have the same number: In this case imagine each person picks their random number in turn. From person one through five, probabilities of picking unique numbers: For person one: 10/10 (since no other numbers have been picked yet) For person two: 9/10 (since one number has been picked by person one) Person three: 8/10 (Assume that persons one and two have picked unique numbers, since we are looking for the prob. that ALL have picked unique numbers) Person four: 7/10 Person 5: 6/10 Multiply together: get 30,240/100,000 = 30.24% Subtract from 100% to get 59.76% (required answer)

Anon has the final correct answer and Lordash has the correct explanation. The problem is a simpler version of the birthday paradox, with alternate ways to solve the problem outlined on this page: http://en.wikipedia.org/wiki/Birthday_problem

lordash is almost right, except that 100% - 30.24% = 69.76%

Interesting

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1-P(all people chose different numbers)