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. Let B be the event that exactly two doors are in the same condition. List the outcomes of B.
[Let "L" designate "locked" and "U" designate "unlocked".]
A) {LLL, LLU, LUL, LUU, ULL, ULU, UUL, UUU}
B){LLU, LUL, ULL}
C) {LLU, LUL, ULL, LUU, ULU, UUL}
D) None of these.

Question

Quizplus · Accepted Answer

B is the event that exactly two doors are in the same condition, so we can eliminate the outcomes where all three doors are either locked or unlocked. That leaves us with four outcomes where two doors are locked and one is unlocked (LLU, LUL, ULL) and three outcomes where two doors are unlocked and one is locked (LUU, ULU, UUL). Therefore, the correct answer is choice C, which lists all seven outcomes that satisfy the event B.

Nanette Must Pass Through Three Doors as She Walks from Her