You have $$200,000$ to invest in a portfolio containing Stock A$,$ Stock B$,$ and a risk$-$free asset.$$ The expected return of Stock A is $15\%$ and its beta is $1\mathrm{.}2.$ The expected return of Stock B is $22\%.$ You will invest $$50,000$ in Stock A$.$ You wish to create a portfolio with an expected return of $25\%$ and a beta of $1\mathrm{.}5.$ What is the beta of stock B$?$