Tiger Funds Ltd. operates a number of mutual funds in high technology and in financial sectors. Hussein Roberts is a fund manager who runs a major fund that includes a wide variety of technology stocks. As fund manager he decides which stocks should be purchased for the mutual fund. The compensation plan for fund managers includes a first-year bonus for each stock purchased by the manager that gains more than $10 \%$ in the first six months it is held. Of those stocks that the company holds, $40 \%$ are up in value after being held for two years. In reviewing the performance of Mr. Roberts, they found that he received a first-year bonus for $60 \%$ of the stocks that he purchased that were up after two years. He also received a first-year bonus for $40 \%$ of the stocks he purchased that were not up after two years. What is the probability that a stock will be up after two years given that $\mathrm{Mr}$. Roberts received a first-year bonus?