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.

MIRB16  Apr 1, 2018

\(\begin{align*} \frac{1}{10}[(1\cdot 2)&+(1\cdot 3)+(1\cdot 4)+(1\cdot 5)+{}\\ &(2\cdot 3)+(2\cdot 4)+(2\cdot 5)+(3\cdot 4)+(3\cdot 5)+(4\cdot 5)]\\ &\qquad\qquad\qquad\qquad=\frac{85}{10} = \boxed{8.5}. \end{align*}\)

lynx7  Apr 1, 2018

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