October 02, 2011

11. Quadractic Quizzicality

11. Quadractic Quizzicality

Question: Suppose B and C are random numbers from a uniform(0,1) distribution. What is the probabilty that x^2 + Bx + C = 0 has two real roots?

Solution: x has two real roots if its discriminant is greater than zero. i.e B^2 - 4C > 0.

So B^2 > 4C or c < B^2/4.

The sample space for B and C has an area of 1 and the area beneath the curve of C = B^2/4 represents the values for B and C that result in real roots.

So the probabilty that B^2 - 4C > 0 (the equation x^2 + Bx + C = 0 has two real roots) is the integral from 0 to 1 of B^2 /4 which is 1/12.


September 16, 2011

Maths Busking

I've just visited www.mathsbusking.com. It comprises of:

"street performance, stage performance, entertainment at educational/scientific events, performer training sessions, teacher development and workshops for young people."

It sounds like great fun and it is definately something I wouldn't mind being invloved in.


Maths Joke

"Divide fourteen sugar cubes into three cups of coffee so that each cup has an odd number of sugar cubes in it."
"That's easy: one, one, and twelve."
"But twelve isn't odd!"
"It's an odd number of cubes to put in a cup of coffee..."

from: http://www.math.ualberta.ca/~runde/jokes.html


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