Question

A large cable company reports the following. 75% of its customers subscribe to cable tv service 41% of its customers subscribe to internet service 38% of its customers subscribe to telephone service 25% of its customers subscribe to both cable tv and internet service 21% of its customers subscribe to both cable tv and phone service 23% of its customers subscribe to both internet and phone service 15% of its customers subscribe to all three services. since this is a large company the outcome for the first customer will have little effect on the outcome for the second customer, calculate calculate p(c1 ∩ c2).

Answer 1

Without further context, calculating P(C1 ∩ C2) is not possible. With additional information, the probability of intersection would refer to the overlap between two services. Example calculation using given data for cable TV and internet services shows a 25% intersection.

Step-by-step explanation:

The student is asking about calculating the probability of the intersection of two events, referred to as P(C1 ∩ C2). However, the question does not specify what C1 and C2 represent, making it impossible to provide a numerical answer. If C1 and C2 are meant to represent two of the services (cable, internet, telephone) offered by the cable company, then more information is needed about which services they refer to. Typically, to calculate P(C1 ∩ C2), you would need to know the individual probabilities of C1 and C2 and the probability of their intersection (which may have been provided in the question).

Since we cannot determine P(C1 ∩ C2) without additional details, let's explore an example using the provided statistics. If C1 represents subscribing to cable TV and C2 represents subscribing to internet service, then the probability of a customer subscribing to both (the intersection of C1 and C2), would be the percentage of customers subscribing to both cable TV and internet service, which is given as 25%. Hence, P(C1 ∩ C2) would be 0.25 or 25%.