Let a and b be chosen at random from {0,1,2,3,4,5,6,7,8,9}.
Find the probability that
x^2 + ax + b^2 = 0 will have
at least one real solution.
Quadratic a^2 + ax + b^2 = 0 has real root(s) if the discriminant is non-negative, i.e.,
a^2 - 4*b^2 >= 0
a^2 >= 4*b^2
As a and b are both non-negative in the set from which they are chosen,
a >= 2*b
What then is the probability that that will be the case?
Overall there are 100 ways in which a and b can be chosen (assuming equality between the two is allowed). How many of these are successes?
b a
0 10 choices
1 8 choices
2 6 choices
3 4 choices
4 2 choices
5 0 choices
--
30
The probability is 30%.
|
|
Posted by Charlie
on 2017-03-01 10:52:32 |
solution (spoiler)
