Weekly puzzles to work your brain!
Random Ratio
If $P$ and $Q$ are two points chosen at random from the interval $(0,1)$, what is the probability (up to two decimal places) that the ratio $P/Q$ lies between $1$ and $2$?
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Solution
Assume that the points are $x$ & $y$ respectively. We want to know if $\frac{x}{y}$ is between $1$ and $2$. If we plot this, the limits are $\frac{x}{y}=1$ and $\frac{x}{y}=2$. Thus, the desired region is the area between lines $y=x$ & $y=\frac{x}{2}$.
This region is 1/4 th of the rest.