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; c: first floor, second floor, third floor, fourth 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, one bathroom, fourth floor, and a lake or no special view? the probability is □ (type an integer or a simplified fraction.)

Explanation:

Step1: Calculate total number of combinations

There are 4 options for A (number of bedrooms), 2 options for B (number of bathrooms), 4 options for C (floor number) and 3 options for D (view). Using the counting principle, the total number of combinations is $4\times2\times4\times3=96$.

Step2: Determine favorable combinations

The person wants one - bedroom, one - bathroom, fourth - floor and a lake or no special view. There is 1 option for one - bedroom in A, 1 option for one - bathroom in B, 1 option for fourth - floor in C and 2 options (lake or no special view) in D. So the number of favorable combinations is $1\times1\times1\times2 = 2$.

Step3: Calculate probability

The probability $P$ of an event is given by the formula $P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$. So $P=\frac{2}{96}=\frac{1}{48}$.

Answer:

$\frac{1}{48}$