Question

A fisherman goes out to the sea twice a day. His first attempt leads to a catch with probability 0.6, and his second attempt leads independently to a catch with probability 0.3. Any catch made is equally likely to be either a big catch worth $1,000 or a standard catch worth $500. Let X be the total revenue (in dollar) made by the salesman at the end of the day. Find the expected value of X.

Answer 1

expected number of catch made in a day =expected catch in first attempt+expected catch in 2nd attempt=1*0.6+1*0.3 =0.9

expected value of a catch =(1000+500)/2 =750

therefore expected value of X =750*0.9 =$ 675