Have you ever wondered how rare things are, like how rare it is to get at least a certain score on a multiple choice test? Or how rare it is to guess a locker combo? Well, you’re in the right place! Here are a few rare things!
- How rare is it to get a 100% on a multiple choice test from guessing?
It is actually not hard to do! Let’s first set some variables. Saying ‘a’ is a list of possible answer s, eg: a=[1,1,2] and ‘q’ is the list of questions, eg: q=[4,4,6]. We can do a simple math expression now to figure it out. Multiply all the values of a and q separately. Keep it as the same value. The percent you will get 100% is: 100(a/q). Let’s do this with our a and q variables. a → 1*1*2=2, and q → 4*4*6=96. Now we do 100(2/96)=2.083%. There you go! For a 20 question test of 4 questions each and 1 answer each, you will have 1²⁰=1, and 4²⁰=1099511627776. Now some “Simple” math to figure out 1/1099511627776=9.09e-13. Multiply that by 100 to get 9.09e-11%. So, no guessing!
- How rare is it to guess a locker combo?
There are 50 numbers on your locker, and you just need the first 2 numbers. So what you would do is (1/50)²=0.0004. Then multiply it by 100 for a percentage. 0.04% would be your total answer. The lockers did not have a little error. From my testing, you can still unlock my locker with a give or take of 1 number. (Eg: if a locker combo is 32-19, then 33-18 would still work.) So there are 3 possible numbers for each turn, so it would become (3/50)² = 0.0036 or 0.36%.
- How rare is it for 2 different rgb displays to display the same static? (24 bits/pixel)
In RGB, there are red, green, and blue colors. Each gets 1 byte or 8 bits. 8 bits with 2 different values each is 82=256. There are 3 colors for 256³, or 16,777,216 different color possibilities. That is our base. For 2 pixels to be the same color, it would be a 1/16,777,216 chance or 0.0000059% chance. But it gets even larger for larger displays. Take a look:
10 x 10:
2.96*10⁻⁷²²
100 x 100:
1.58*10⁻⁷²,²⁴⁷
256 x 256:
1.75*10⁻⁴⁷³,⁴⁷⁹
1366 x 768:
8.83*10⁻⁷,⁵⁷⁹,³⁶⁶
HD (About 1 megapixel, 1280 x 720):
7.17*10⁻⁶,⁶⁵⁸,³⁰¹
1080p/Full HD (1920 x 1080):
1.5*10⁻¹⁴,⁹⁸¹,¹⁷⁹
2K (2560 x 1440):
2.65*10⁻²⁶,⁶³³,²⁰⁷
4K/Ultra HD (3840 x 2160):
5.06*10⁻⁵⁹,⁹²⁴,⁷¹⁶
8K (7680 x 4320):
6.59768*10⁻²³⁹,⁶⁹⁸,⁸⁶⁶
1 Gigapixel (1,000,000,000 Pixels, about 31,623 x 31,623):
1 × 10⁻⁷,²²⁴,⁸²¹,⁹⁷⁴
365 Gigapixel image (World Record, About 365,000,000,000 Pixels, About 604,152 x 604,152 resolution):
3 × 10⁻²,⁶³⁷,⁰²²,⁷⁶²,⁰¹⁶ or a 3 followed by about 2.6 trillion zeros.
1 Terapixel (1,000,000,000,000 Pixels, 1,000,000 x 1,000,000):
3.5 × 10⁻⁷,²²⁴,⁷¹⁹,⁸⁹⁵,⁹³⁵ or a 3.5 followed by 7.2 Quadrillion zeros.
