Suppose the amount of time it takes for a computeralgorithm to solve a random puzzle in 1 hour is a random variable X taking values in [0,1] with p.d.f. f(x)

=1/2x where x is measured in hours. What is the probability that a random puzzle will take between 20 and 40 minutes (1/3 to2/3 hours) to solve? \sqrt{\frac{2}{3}}-\sqrt{\frac{1}{3}} \approx 0.239 \sqrt{\frac{2}{3}} \approx 0.816 \sqrt{\frac{1}{3}} \approx 0.577 \frac{1}{3} \approx 0.333