Probability calculation: Determine the probability that you pick a defective calculator 
One company has $3$ locations where they produce calculators. In
  total, the company produced $10000$ calculators. $2750$ of them were
  produced in the first location, $4300$ in second location and $2950$
  at the third location. From $2750$ produced calculators in first
  location, $59$ are defective. In the second location, $85$ of $4300$
  produced calculators are defective and in the third location $125$ of
  $2950$. Determine the probability that you pick a defective calculator
  from the $10000$ produced calculators.

I am not sure how this question can be solved. At first, I just concentrated on each location itself.
If we only look at location one, we have a probability of $\frac{59}{2750}$ to a defective calculator.
In location two we have $\frac{85}{4300}$ and in location three we have $\frac{125}{2950}$.
However, now we want the probability to pick one defective calculator from $10000$ produced calculators. I don't know if my logic is correct but I would simply sum up the single probabilities I just calculated, so we have
$$\frac{59}{2750}+\frac{85}{4300}+\frac{125}{2950} \approx 0.08359 \approx 8.36\text{%}$$
If I just look at the result, it does not seem very realistic. Should the answer not be lower?
 A: There are $10000$ calculators, $59+85+125 = 269$ of which are defective. The probability of picking a defective calculator thus equals:
$$\frac{269}{10000} = 0.0269$$
If $A_i$ is the event in which a calculator is produced in factory $i$ and $D$ is the event in which a calculator is defective, this probability can also be calculated as:
$$P[D] = P[A_1] P[D | A_1] + P[A_2] P[D | A_2] + P[A_3] P[D | A_3] =$$
$$\frac{2750}{10000}\frac{59}{2750} + \frac{4300}{10000}\frac{85}{4300} + \frac{2950}{10000}\frac{125}{2950} = \frac{269}{10000} = 0.0269$$
A: I think your error comes from misunderstanding the question:
your mistake lies in the question's last line - "Determine the probability that you pick a defective calculator from the $10000$ produced calculators."
What you have done by calculating $$\frac{59}{2750}+ \frac{85}{4300}+ \frac{125}{2950}$$ 
is to find the fraction of calculators that are defective out of the calculators that are produced, but not in total.
A better approach to calculate the probability $$P(defective) = \frac{defective}{total}$$
(as suggested by @jvdhooft). Since there are $59+85+125$ defective calculators in total in the $3$ factories, and there are $10000$ calculators in total, you can simply find $$\frac{59+85+125}{10000}$$
