How to pick random items through cumulative probability?

Exercise Background

The exercise consists in generating a 2D map with a user given x,y size of said map, and then place on each cell of the map random items from a table. I have a cell in an [x, y] coordinate of an Items matrix and I have to pick items randomly for every cell of this matrix.

My Problem

I have to select random items from a table of 4 items that have their probabilities shown in cumulative probability, and a cell that has such items can have more than 1 and different combinations of those items.

I don't really know how to go about this problem, taking in account that 2 of the items have the same probability on the given table for the homework.

This is the table of probability given:

Food - 1
Weapons - 0.5
Enemy - 0.5
Trap - 0.3

My Items enumeration:

[Flags]
enum Items
{
    Food = 1<<0,
    Weapon = 1<<1,
    Enemy = 1<<2,
    Trap = 1<<3
}

Again, the expected output is to pick randomly through this percentages what items does 1 cell have. What I'd like to have as an answer would be just a start or a way to go about this problem please, I still want to try and do it myself, avoid complete code solutions if you can.