A financial analyst estimates that the probability that the economy will experience a recession in the next 12 months is 25%. She also believes that if the economy encounters a recession, the probability that her mutual fund will increase in value is 20%. If there is no recession, the probability that the mutual fund will increase in value is 75%. Find the probability that the mutual fund’s value will increase.
P(mutual fund value increases) = P(mutual fund increases | recession) + P(mutual fund increases | no recession) So the answer is 0.2*0.25+0.75*0.75 = 0.05+0.5625= 61.25% Try drawing the probability tree diagram to make it clear.