In this video Sal explains why there is a high probability that 2 people in a room of 30 (which is a potential size of a classroom) may share a birthday. He explains the pattern created by the calculations which find the probable percent of 2 or potentially more people in a room with the same birthday.
He considers the 365 days in a year that person 1 could be born on which is 1. Person 2 would therefore only has 364 possible days for a different birthday. That pattern would continue eg. person 3 – 363 days, person 4 – 362 days, person 5 – 361 days etc.
Sal states that, since this is only for 30 people, the number of days of each of the 30 people get multiplied over the number of days in the year (365) to the power of 30 as that’s how many people there are.
But that gives us the probability that no one would share a birthday so he shows it more simply with factorials which is also much easier to type into a calculator.
It can be written as 365!/(365-30)! = .2937 therefore equaling a 29.37% probability that no one in the class shares a birthday.
So… the probability that 2 or more people in a room of 30 is all the people minus the probability that no one shares a birthday which is 100% – 29.37% = 70.63%
In a room of 30 people there is a 70.63% chance 2 people share a birthday
I believe it is an interesting concept to teach children. It would provide them with the ability to connect the notion of patterns throughout mathematics and link it to other areas to gain a greater understanding. Other skills are also gained through doing this such as calculator skills, the use of percentages and basic arithmetic. Mathematics is connected in many ways and these skills can be transferred to other areas.
