according to a survey, 67% of households have cable tv, 74% of households have 2 or more tv sets, and 55% of households have cable tv and two or more tv sets.
a) what is the probability that the household has cable tv and only one set of tv?
b) if the random chosen household has 2 or more tv sets, what is the probability that the household also has cable tv?

Question

according to a survey, 67% of households have cable tv, 74% of households have 2 or more tv sets, and 55% of households have cable tv and two or more tv sets. 
a) what is the probability that the household has cable tv and only one set of tv?
b) if the random chosen household has 2 or more tv sets, what is the probability that the household also has cable tv?

kropot72 · Answer

a) The probability that a household with cable tv has one or more tv sets is the same as the probability that the household has cable tv (at least one tv set is needed to watch cable tv).
The events 'cable tv and only one tv set' and 'cable tv and two or more tv sets' are mutually exclusive. Therefore
P(ctv + 1 or more tv sets) = .67 =.55 + P(ctv + only 1 tv set)
P(ctv + only 1 tv set) = .67 - .55 = .12