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 Mr. Roberts received a first-year bonus?