1. The probability that next month an ombudsman of a university receives no complaints from a freshman...
Question:
1. The probability that next month an ombudsman of a university receives no complaints from a freshman is 0.73. Otherwise, the number of complaints from the freshmen is a normal random variable with mean 2 and standard deviation 3. The probability that next month the ombudsman receives no complaints from a sophomore is 0.53. Otherwise, the number of complaints from the sophomores is a normal random variable with mean 3 and standard deviation 4. Assuming that complaints from freshmen are independent of complaints from sophomores, find the probability that next month the number of complaints from freshmen is greater than the number of complaints from sophomores.
Hint: Let A be the event that next month the ombudsman will receive at least one complaint from a freshman. Let B be the event that next month he or she will receive at least one complaint from a sophomore. Let C be the event that nextmonth the number of complaints by the freshmen is greater than the number of complaints by the sophomores.
The probability that we are interested in is P(ABc)+P(ABC). Use the multiplication rule to calculate P(ABC).
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