SOLUTION: There are 20 people in a room, and each of the 20 writes down an integer at random from 1-100 inclusive. Find the probability that at least two people wrote down the same number. E

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Question 1028530: There are 20 people in a room, and each of the 20 writes down an integer at random from 1-100 inclusive. Find the probability that at least two people wrote down the same number. Express your answer as a decimal rounded to four significant digits.
This is not so complicated; however, how do I "determine the probability of AT LEAST TWO PEOPLE" drawing the same number?
Thank you in advance!!
By the way, the answer is 0.8696
Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
There are 100 P 20 = 1.303995*10^39 different ways to have 20 people pick different numbers (from a pool of 100). No repeated numbers allowed.

Note: 100 P 20 is referring to a permutation

There are 100^20 = 1*10^40 different ways for 20 people to pick any number they want (repeats are now allowed)

The probability of 20 people picking different numbers (no repeats) is
(1.303995*10^39)/(1*10^40) = 0.1303995

Subtract this from 100%, which is equivalent to the decimal form 1.00, so

1.00 - 0.1303995 = 0.8696005 which rounds to 0.8696

I'm subtracting from 100% because there are 2 choices
either you have a case where everyone picks different numbers (no repeats)
OR
there is a case where some people pick the same number(s) (repeats allowed). Whether who or how many, it doesn't matter.
There are no other possible cases. These two probabilities add to 100%

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Therefore, the final answer is approximately 0.8696 which is approximately 86.96%

Answer by ikleyn(52794) (Show Source):
You can put this solution on YOUR website!
.
There are 20 people in a room, and each of the 20 writes down an integer at random from 1-100 inclusive. Find the probability that at least two people wrote down the same number. Express your answer as a decimal rounded to four significant digits.
This is not so complicated; however, how do I "determine the probability of AT LEAST TWO PEOPLE" drawing the same number?
Thank you in advance!!
By the way, the answer is 0.8696
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1. The full set of outputs is the set of all functions defined on 20 points and taking 100 values. The cardinality of this set is N = . 2. In how many ways can 20 people write 20 different numbers? Take and multiply by 20!: you will get the number of ways M = 100*99*98* . . . *82*81. 3. Now the probability under the question is . It is the same as this number .