Fun with Math
from Mobile team March (many years ago) sharing
1. Is 0.999… = 1? Answer Yes
1/9 = 0.111…..
multiply by 9
9 * 1/9 = 9 * 0.111…
1 = 0.999…
QED
2. What’s wrong with this proof?
From the fourth line to the fifth, both sides are divided by (a-b), which is zero because a = b
3. What’s wrong with this proof?
From the fourth line to the fifth (again), in order to change from sqrt(a / b) to sqrt(a) / sqrt(b), the condition it has to meet is a, b > 0
4. Birthday Paradox
Simply said, you and your friend are gonna bet whether there are people in the room that share the same birthday. How many people are in the room that will make you bet on `yes`?
Since there are 366 possibilities for birthdays, most people answer more than 100. Actually, if there are only 23 people, the chance to have shared-birthday people is more than 50%!!
Calculation:
First, you add a person into the room. The chance is 0%
Next, you add the second one. The chance of they don’t share a birthday is 365/366.
Then the third one. The chance of no one share birthday becomes (365 / 366) * (364 / 366)
So at the nth person, the chance that everyone has different birthday is (1/366)^n * (365 * 364 * 363 * … * (366-(n-1)), which is 0.492703 for n = 23. That’s less than 50%!
All the chances are in this table
Only 40 people in the room, a chance to have the same birthday is almost 90%
Go bet with your bad-at-math friends!!
