Question

1 point) Let A, B, and C be independent random variables, uniformly distributed over [0,5], [0,15], and [0,2] respectively. What is the probability that both roots of the equation Ax2+Bx+C=0 are real?

Answer 1

SOLUTION:

From given data,

Let A, B, and C be independent random variables, uniformly distributed over [0,5], [0,15], and [0,2] respectively.

Ax²+Bx+C=0

For real solution

B² - 4 AC > 0

B² > 4 AC

Since

A = [ 0,5]

B = [0,15]

C = [0,2]

B² > 4 AC

so we can square root both side

B> 2  

Also , maximum value of  2  

= 2  

= 2

Which is less than maximum value of B = 15

Limits

0 < A < 5

0 < C < 2

2   < B < 15

Volume over which we are integrating:

5*2*15 =  150

So you must divide by 150

  

= 1/150 * 121.89087

P = 0.8126058