Consider the light bulb problem. Suppose we do not necessarily want to wait for the light bulb to burn out before we make a decision as to which type of bulb is being tested. Therefore, a modified experiment is proposed. The light bulb to be tested will be turned on at 5 pm on Friday and will be allowed to burn all weekend. We will come back and check on it Monday morning at 8 am and at that point it will either still be lit or it will have burned out. Note that since there are a total of 63 h between the time we start and end the experiment and we will not be watching the bulb at any point in time in between, there are only two possible observations in this experiment ( the bulb burnt out ↔ { X < 63}) or ( the bulb is still lit ↔ { X < 63}).
(a) Given it is observed that the bulb burnt out over the weekend, what is the probability that the bulb was an - type bulb?
(b) Given it is observed that the bulb is still lit at the end of the weekend, what is the probability that the bulb was an type bulb?