May you please show me the work to find the st. dev for both A and B as the solution provided above only gives the answer (32.27 and 21.51) without showing the steps

16. (LO 8.4) To achieve a zero standard deviation for a portfolio, calculate the weights of stock A and stock B, assuming the correlation coefficient is -1. State of the Probability of Expected Return on Stock A in Expected Return on Stock B in Economy Occurrence This State This State High growth 25% 55% Moderate growth 20% 20% 25% Recession -10% -20% 40% 55% OB = Solution: 32 .27 W + 21.51 + 32.27 WB= 1-WA= 10.6 = 0.4 = 0.6