Consider a system of only three securities: S1, S2, S3. Currently their unit prices are $20, $23 and $25, respectively. Suppose after one month, there are only the following three outcomes:

W1 :(S1, S2, S3) = (40, 23, 30)

W2 :(S1, S2, S3) = (20, 23, 24)

W3 :(S1, S2, S3) = (10, 23, 20)

(a) (15 points) Find the risk-neutral probabilities for the three states: W1, W2 and W3. (b) (15 points) Price a European put option with underlying stock S1 and strike $30.