# Need help with Expected Return and Joint Probability problem

I’m doing Concept Checkers section of Reading 9 - Probability Concepts in Schweser and there’s the following question I don’t understand

Given the Joint Probability table like the picture below

The expected return of Stock A is: 0.08

I checked the answer section but I don’t understand why they can come up with this answer. The formula being used is: 0.4*(-0.1)+0.3*0.1+0.3+0.3=0.08

First, there’s an error in your formula (likely just a typo):

E® = 0.4 × (−0.1) + 0.3 × 0.1 + 0.3 × 0.3 = 0.08

The probability that Stock A has a return of −10% is 0.4 (add up the probabilities in the first row of the table). The probability that Stock A has a return of +10% is 0.3 (add up the probabilities in the second row of the table). The probability that Stock A has a return of +30% is 0.3 (add up the probabilities in the third row of the table). Therefore, the expected return is:

E® = [P(−10%) × (−10%)] + [P(+10%) × (+10%)] + [P(+30%) × (+30%)]

= 0.4 × (−0.1) + 0.3 × 0.1 + 0.3 × 0.3 = 0.08 = 8%

which is exactly the formula you quoted (after the typo’s fixed).