A Financial Analyst estimates that the probability that the economy will experience recession in next
one year is 30%. He also believes that in case of recession, the probability that his mutual funds will
increase in value is 20%. He also believes that if there is no recession the probability that the value of
mutual funds will increase in value is 75%. Find the probability that mutualfunds value will increase.

Probability that recession will happen = 0.3 and probability that value will increase in this case = 0.2
Expected probability of mutual fund value increase in this case = 0.3*0.2 = 0.06

Probability that recession will not happen = 1 - 0.3 = 0.7 and probability that value will increase in this case = 0.75 
Expected probability of mutual fund value increase in this case = 0.7*0.75 = 0.525

Hence, total expected probability that mutual fund value will increase = 0.585