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Question

I have 5 marbles numbered 1 through 5 in a bag. Suppose I take out two different marbles at random. What is the expected value of the product of the numbers on the marbles? Answer as a decimal to the nearest tenth.

Accepted Answer

There are 52 = 10 different pairs of marbles that can be drawn, and the expected value of the product is the average of the products of each pair. This is align* 110[(1 2)&+(1 3)+(1 4)+(1 5)+ &(2 3)+(2 4)+(2 5)+(3 4)+(3 5)+(4 5)] &=8510 = 8.5. align*