not necessarily. even if the expected value of taking a risk is positive, taking the risk can be undesirable, e.g. due to large variance. statistical distribut

not necessarily. even if the expected value of taking a risk is positive, taking the risk can be undesirable, e.g. due to large variance. statistical distributions that include a risk aversion parameter exist precisely to model this kind of problem (unfortunately their names have slipped my mind, otherwise I'd provide links)