Chris tries to throw a ball of paper in the wastebasket behind his back (without looking). He estimates that his chance of success each time, regardless of the outcome of the other attempts, is 1/3. Let X be the number of attempts required. If he is not successful within the first 5 attempts, then he quits, and he lets X = 6 in such a case.
Let Aj be the event containing all outcomes in which "j or more attempts" are required to get the basket. Let Xj indicate whether Aj occurs. Then X = X1 + X2 + X3 + X4 + X5 + X6. Find the expected value of X by finding the expected value of the sum of the indicator random variables.