the probability that a civil servant owns a car is 1/6, of two civil servants, C and D, what is the probability that only 1 owns a car?

Question

anonymous · Answer

Is the probability 5/18?

sasogeek · Answer

the book says it's 1/3, i had 5/18 -_-

anonymous · Answer

sometimes books are wrong but the number above i don´t think it might be 5.. because it´s asking the probability of 1, so...unless..well idunno...

anonymous · Answer

1/6 + 1/6 = 1/12 / 2 = 1/12 *1/2 = 1/24  God. what am I doing? but.. is this the probability of have or not a car..

sasogeek · Answer

if only one has a car, then when C has a car, D doesn't have a car, and when D has a car, C doesn't. probability that C or D has a car is 1/6 and probability that C or D do not have a car is 5/6

if only one has a car, then the following statement is true
$$\large (CnD^') U(C^'nD) =(\frac{1}{6}\times \frac{5}{6})+(\frac{5}{6}\times\frac{1}{6})=\frac{5}{36}+\frac{5}{36}=\frac{10}{36} $$$$\large =\frac{5}{18} $$