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Probability: High Risk Apartments

In a local town, there are three separate apartment blocks, A, B and C. Block A contains 10 apartments, of which two contain "High Risk" inhabitants. Block B contains eight apartments, with three occupied by "High Risk" inhabitants, and Block C contains 12 apartments, with four "High Risk" apartments.

Assume that an apartment in Block B was visited, and found to be a "High Risk" apartment. If the Fire Brigade now wishes to visit another apartment, again to be selected at random from all three blocks, what is the probability that the second flat will not be "High Risk"?

Solution Preview

The probability that the second flat will not be "High Risk" is the ratio of the number of remaining apartments that are not "High Risk" to the total number of remaining apartments. The reason why both of the numbers in the ratio include only the remaining apartments is that the Fire Brigade wishes to visit "another" apartment (that is, some apartment other than the one they have already visited).

Well, let's see how many apartments are ...

Solution Summary

The "formula" for the probability of the indicated outcome is provided. Then the individual components of that outcome are examined (and explained in detail), and are used to compute the answer.