Question

an apartment complex offers apartments with four different options, designated by a through d. there are an equal number of apartments with each combination of options.
a
one bedroom
two bedrooms
three bedrooms
four bedrooms
b
one bathroom
two bathrooms
three bathrooms
c
first floor
second floor
third floor
d
no special view
golf course view
lake view
if there is only one apartment left, what is the probability that it is precisely what a person is looking for, namely one bedroom, two bathrooms, third floor, and a lake or golf course view?

Explanation:

Step1: Calculate total number of combinations

For option A (bedrooms), there are 4 choices; option B (bathrooms), 3 choices; option C (floors), 3 choices; option D (views), 3 choices. Total combinations: \(4\times3\times3\times3 = 108\).

Step2: Calculate favorable combinations

For the desired apartment: A (1 choice: one bedroom), B (1 choice: two bathrooms), C (1 choice: third floor), D (2 choices: lake or golf view). Favorable combinations: \(1\times1\times1\times2 = 2\).

Step3: Calculate probability

Probability is favorable over total: \(\frac{2}{108}=\frac{1}{54}\).

Answer:

\(\frac{1}{54}\)