Search for question

the course of a year, the effectiveness of this feature is observed. For 40% of the users, the feature doesn't work as intended, leading to an average of 5 song repetitions in a year. However, for the users for whom the feature works effectively, the average number of song repetitions per year is reduced to 2. The number of repetitions per year can be modelled by a Poisson random variable. Calculate: (a) The probability that a user experiences exactly 1 song repetition in a year if they are among those for whom the feature works effectively. (b) The probability that a user experiences exactly 1 song repetition in a year if they are among those for whom the feature does not work effectively. (c) The overall probability that a randomly chosen user from the service experiences exactly 1 song repetition in a year. (d) The conditional probability that a randomly chosen user is among those for whom the feature works effectively, given that they experienced exactly 1 song repetition in the trial year.

Fig: 1