A CD has a 5% chance of being a smash hit and profiting $5.2 million, a 50% chance of being a modest success and profiting $0.9 million, and a 45% chance of being a flop and breaking even. What is the expected earnings value of the CD?

Question

Mathematics

Gabriella James

21 July, 15:26

A CD has a 5% chance of being a smash hit and profiting $5.2 million, a 50% chance of being a modest success and profiting $0.9 million, and a 45% chance of being a flop and breaking even. What is the expected earnings value of the CD?

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Answers (1)

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Ayla Hines · Answer 1

P (S) = Probability of Smash = 0.05 (5%)

P (M) = Probability of Modest = 0.5 (50%)

P (F) = Probability of Flop = 0.45 (45%)

If I'm not mistaken, we should use the discrete random variable model,

so the expected earnings would be:

E (X) = (0.05 * 5.2) + (0.5 * 0.9) + (0.45 * 0)

= 0.26 + 0.45 + 0

= 0.71 Mill'