I want to choose a random item from a set, but the chance of choosing any item should be proportional to the associated weight

Example inputs:

item                weight
----                ------
sword of misery         10
shield of happy          5
potion of dying          6
triple-edged sword       1

So, if I have 4 possible items, the chance of getting any one item without weights would be 1 in 4.

In this case, a user should be 10 times more likely to get the sword of misery than the triple-edged sword.

How do I make a weighted random selection in Java?

java random double
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