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A slot machine can display the numbers 1, 2 or 3. 1 has probability 0.1, 2 has probability 0.3, and 3 has probability 0.6. The machine is run 10 times, and the numbers that show are added. At the end you get as many dollars as the sum indicates. What are the expected winnings?

My thoughts were to find the expected value of winnings for one trial and then multiply it by 10. So $E(x)=1*0.1+2*0.3+3*0.6 = 2.5$ then since we ran it 10 times the expected winnings would be 25. Would this be correct or no?

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If the draws are independent, this is correct.

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