Acontractor is considering a sale that promises a profit of $23000 with a probability of 0.7 or a loss (due to bad weather, strikes, and such) of $12,000 with a probability of 0.3. what is the expected profit?

The expected value (or expected profit in this case) is X = ∑xₙpₙ, where xₙ is the "outcome" ( in this case, winning or losing money) and pₙ is the probability of such outcome.

then, If you have a 0.7 chance of winning $23000, and a 0.3 chance of losing $12.000, the expected value is : 0.7*$23000 - 0.3*$12000 = $12500.

So the expected profit is $12500.