To generate a phone bill, observe the duration of the call in integer minutes (rounding up). Charge for m=1,2,3,… minutes if the exact duration is m−1<≤m. Let m denote the event that a call is billed for m minutes. The probability of each event m is:

P[m]=(1−)m−1where=1−(0.54)1/3≈0.186 .

a. Classify a call as long () if the call lasts more than three minutes,. What is P[L]?
b. What is the probability that a call will be billed for nine minutes or less?