3. Bill assembles toys in a factory. The assembly time of each toy is exponentially distributed with mean of 6 minutes, independently of previous assembles. (a) What is the probability that the assembly time of the fourth toy is less than 6 minutes? (b) For each toy that Bill assembles in less than 6 minutes, Bill receives a bonus. What is the the expected number of bonuses that Bill receives among the 100 toys? (c) Bill's daughter arrives at the factory an hour after Bill starts working. She stays there for either 2, 3, or 4 minutes, with probability 1 / 3, each (independently of her dad's progress). What is the probability that she will see her dad nishes assembling a toy, while she is there? (d) Assume that with probability 1/10 Bill assembles a toy incorrectly, independently of previous assemblies. Given that in the rst hour there is exactly one toy that Bill assembled incorrectly, what is the probability he assembled a total of 10 toys in the rst hour and 10 toys in the next hour? (e) What is the distribution of the number of toys that Bill managed to assembled in the rst 20 minutes, if it known that at time t = 0 Bill started working, and within the rst hour, Bill assembled 15 toys? (f) What is the expectation of the number of toys that Bill managed to assembled in the rst 20 minutes, if it known that at time t = 0 Bill started working, and between minute 10 and 60 Bill assembled 15 toys? (4+4+4+4+4+5=25 points)