Six people are asked to pick a number from 1 to 20. What is the probability that at least two people will pick the same number?
Please help. Thanks
read up on the birthday problem: the chance that two will share a birthday.
To find the probability that at least two people will pick the same number, you can use the complement rule.
First, let's find the probability that no two people pick the same number.
For the first person, there are 20 possible numbers they can choose.
For the second person, there are only 19 remaining numbers to choose from (since they can't choose the same number as the first person).
For the third person, there are 18 remaining numbers, and so on.
Therefore, the probability that no two people pick the same number is:
(20/20) * (19/20) * (18/20) * (17/20) * (16/20) * (15/20)
Now, to find the probability that at least two people pick the same number, we can subtract the probability of no two people picking the same number from 1.
Probability of at least two people picking the same number = 1 - Probability of no two people picking the same number
Probability of at least two people picking the same number = 1 - [(20/20) * (19/20) * (18/20) * (17/20) * (16/20) * (15/20)]
Calculating this expression will give you the probability that at least two people will pick the same number.