2. Malia collected information about whether the members of the 36 households on her block subscribed to cable television and home phone services. Her results are shown in the table below.nIf a household on Malia's block is selected at random and does subscribe to cable television, what is the probability the members of the household also subscribe to home phone service?
Answer: A
The probability that a household subscribing to cable television also subscribes to home phone service is 14/18.
In Malia's data, 14 out of the 18 households that subscribe to cable television also subscribe to home phone service. Therefore, the probability is calculated as the ratio of these two numbers.
A) 14/18
This option is correct because it accurately represents the fraction of households that subscribe to both cable television and home phone service out of those that subscribe to cable television. The count of households subscribing to both services is 14, and the total number of households with cable is 18.
B) 14/26
This option is incorrect as it suggests that there are 26 households that subscribe to cable television. The total number who subscribe to cable television is only 18, making this ratio inaccurate.
C) 18/36
This option is also incorrect. While 18 is the number of households that subscribe to cable television, this fraction does not reflect the number of households that also subscribe to home phone service. The total number of households is 36, but the relevant total for the probability calculation must be only those who subscribe to cable.
D) 14/36
This option is incorrect because it implies that the probability is based on the total number of all households (36) rather than just those that subscribe to cable television (18). The numerator should reflect the 14 households that subscribe to both services.
Conclusion
The correct answer, 14/18, effectively captures the probability of a household subscribing to home phone service given that they already subscribe to cable television. All other options fail to provide the correct context or numbers necessary for calculating the probability as required by the question.