How can you use the properties of multiplication to determine what the factors are
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The rigorous way to do this would be to compute a few integrals, but less work is usually better. Each of these probabilities correspond to the areas of rectangles. Each rectangle will have a height of 1, and the probability of interest will tell you everything you need to know about their lengths.
Alternatively, you can use the fact that
to get the same result.
Alternatively, you can use the fact that