This week we planned to shift our WOW experiment outdoors.
We bought some bottle caps and threw them randomly on the floor. They landed in different positions. Some of them fell with their open sides up, some had their open sides down while a few landed on their vertical sides. We were curious, as to how many of the 2000 bottle caps would have landed in which positions of the three. But we were too lazy to count.
Can math help us here?
Yes, it did!
Out of our laziness, we choose a math's trick here. We used probability to find out the orientation of the caps. Instead of throwing 2000 caps again. We threw a single cap multiple times and noted its chances of falling in either of the three orientations.
After 25 counts we noted that 13 times the bottle caps landed with their open sides up, 7 times their open sides were facing the floor and 5 times they fell vertically on their sides. After another 75 counts, the stats were: 67 with open sides up, 23 with open sides down and 10 standing vertically.
We had tried 100 times by now. We thought of counting 100 falls more. After 200 counts, 134 caps had fallen with their open sides up, 47 with open sides down and 19 were standing vertically.
The caps which fell with their open sides up were in majority. The probability of these caps was :
134\200 = 0.67
It was easy from here. We had our magic number '0.67' now!
To find out the probability of the caps fallen with their open sides up out of the 2000 caps we simply had to multiply.
Probability of caps with open sides up = 2000 x 0.67 = 1340
Thus, most probably 1340 caps out of 2000 would have landed with their open sides up.
To verify our results we had to get over our laziness and count the 2000 bottles caps on the floor. Here's what we found :
Caps with open sides up: 1360
Caps with open sides down: 60
Caps standing vertically: 180
Can you now guess what could have been the probability if we would have thrown 600 bottle caps?
Watch the video below for understanding.
What is OD WOW Series?
Math and Science are filled with wonders. At Open Door, we asked ourselves: How do we bring out the Wow! factor in these concepts? This search for Wow led to the start of a new initiative - Open Door's Wow series! This is a series of content videos for Math and Science enthusiasts.
OD WOW Series aims at bringing the wonders behind concepts into limelight and to use the power of appreciation to enrich the learning. It is a series of videos on Math and Science concepts with simple setup hands-on experiments designed and conducted by OPEN DOOR Team. You can access all the videos, every fortnight on Open Door YouTube Channel.
We proudly announce the LAUNCH!
Bombay Scottish School, Mumbai, one of the top schools in India has been using Open Door’s Mastery Assessments program for many years. Recently, a mastery cycle was completed and 10 – 15% improvement was noticed in learning outcomes.
Watch the first video from 'Open Door's Wow series' that explores the question: Can solids apply a buoyant force? We put four balls in a bucket of rice. Then, we started shaking the bucket. Guess what has happened after some time?