4.6. Rockets are launched until the first successful launching has taken place. If this does not occur within 5 attempts, the experiment is halted and the equipment in- spected. Suppose that there is a constant probability of 0.8 of having a successful launching and that successive attempts are independent. Assume that the cost of the first launching is K dollars while subsequent launchings cost K/3 dollars. Whenever a successful launching takes place, a certain amount of information is obtained which may be ex- pressed as financial gain of, say C dollars. If T is the net cost of this experiment, find the probability distribution of T.