Step 1 :The expected value E(X) of a probability experiment is calculated by multiplying each outcome by its probability and then summing these products. The formula is given by E(X) = X1*P(X1) + X2*P(X2) + X3*P(X3)
Step 2 :Substitute the given values into the formula: E(X) = $10*(3/8) + $4*(1/8) + $2*(4/8)
Step 3 :Perform the multiplication: E(X) = $30/8 + $4/8 + $8/8
Step 4 :Add the fractions: E(X) = $42/8
Step 5 :Simplify the fraction to get the final answer: \(\boxed{E(X) = $5.25}\)