Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked.
List the outcomes of the sample space.

A) $\{\mathrm{LLL}, \mathrm{UUU}\}$
B) $\{ \mathrm { LLU } , \mathrm { LUL } , \mathrm { ULL } , \mathrm { UUL } , \mathrm { ULL } , \mathrm { LUU } \}$
C) $\{ \mathrm { LLL } , \mathrm { LLU } , \mathrm { LUL } , \mathrm { LUU } , \mathrm { ULL } , \mathrm { ULU } , \mathrm { UUL } , \mathrm { UUU } \}$
D) None of these.

Question

Nanette must pass through three doors as she walks from her company's foyer to her office. Each of these doors may be locked or unlocked.
List the outcomes of the sample space.

A) $\{\mathrm{LLL}, \mathrm{UUU}\}$
B) $\{ \mathrm { LLU } , \mathrm { LUL } , \mathrm { ULL } , \mathrm { UUL } , \mathrm { ULL } , \mathrm { LUU } \}$
C) $\{ \mathrm { LLL } , \mathrm { LLU } , \mathrm { LUL } , \mathrm { LUU } , \mathrm { ULL } , \mathrm { ULU } , \mathrm { UUL } , \mathrm { UUU } \}$
D) None of these.

Quizplus · Accepted Answer

The sample space for the three doors consists of all the possible outcomes of the three doors being either locked (L) or unlocked (U). 
For the first door, there are two possibilities: L or U.
For the second door, there are again two possibilities, since the first door being locked or unlocked does not affect the second door: L or U.
For the third door, there are once again two possibilities, since the state of the first and second doors does not affect the third door: L or U. 
Therefore, the total number of outcomes is $2\cdot2\cdot2=8$, which are exactly the outcomes given in choice C.

Nanette Must Pass Through Three Doors as She Walks from Her