Answer for Day 1 Math Problem

86.96% 🎯

Solution

The problem is actually similar to the Birthday Paradox problem, except that this problem has 100 possible numbers for each person instead of 365 (or 366 in leap years where February 29 is included).

The general formula is the following.

P(n) = 1 - (c! / (c^n * (c - n)!))

where

• P(c) = probability of at least two people having the same chosen number
• c = quantity of numbers that can be chosen
• n = number of people who chose a number

Our equation now is the following.

P(20) = 1 - 100! / (100^20 * (100-20)!)

which when evaluated has the result of 86.96%.

The birthday paradox is fun! Maybe invite 15 people on D.Buzz to choose a number from 1 to 50 (without others knowing their choice before showing everyone's results) and be surprised that there is 90.35% chance any two people have the same number!

Winner: none 🤯

1 HIVE has been reserved for the next day there is a winner. 🏧 This means that 2 HIVE will be awarded to the next winner for this Math mini-contest! 😃

@minus-pi was close to the correct answer! He forgot to deduct his answer from 1, so his answer will be correct if he is referring to the probability that there will be no participants sharing the same number. 😀

Mentions: @jfang003, @ahmadmanga (@ahmadmangazap), @holovision, @eturnerx (@eturnerx-dbuzz), @appukuttan66, @dkmathstats, and @paultactico2 🤓
Special mentions: @dbuzz, @chrisrice, @jancharlest, and @mehmetfix 🤯