The City Housing Authority has received 100 applications from qualified applicants for ten low-income apartments. Five of the apartments are on the north side of town, and five are on the south side. If the apartments are to be assigned by means of a lottery, find the following probabilities. Two specific qualified applicants will be selected for apartments on the same side of town. (Round your answer to five decimal places.)

Question

anonymous · Answer

You're looking at the probability of two events. The first event is one specific applicant being selected for an apartment. The second event is another specific applicant being selected for an apartment on the same side of town. If the apartments are given out by lottery, a specific applicant has a 10% chance of being selected. For the second event, we're looking at a dependent probability, where there are four apartments left on the side of town in question, and 99 applicants left in the pool. That probability will be 4/99. Multiply the two to find the total probability.

anonymous · Answer

Thanks. i was struggling with that one.

anonymous · Answer

Yeah, dependent probabilities can be tough. The most common pitfall is thinking that the first person has to be selected for one on a certain side of town. Whichever side of town they get selected for, then the other person just has to match.