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.**

Ax^{2}+Bx+C=0

For real solution

B^{2} - 4 AC > 0

B^{2} > 4 AC

Since

A = [ 0,5]

B = [0,15]

C = [0,2]

B^{2} > 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

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