Question

Amanda is a cabinetmaker. She makes cabinets using one of three types of wood: birch, maple, or cherry. She can finish each type of wood with either transparent or semitransparent stain. For knobs, Amanda uses bronze, steel, or wood.
The probability that Amanda uses birch wood and bronze knobs to make a cabinet is .

The probability that Amanda uses only wood knobs to make a cabinet is ____.

The probability that Amanda uses transparent stain to finish a cabinet is ____.

The probability that Amanda uses cherry wood and semitransparent stain to make a cabinet is _____.

Answer 1

Assume that each material in each category has an equal chance of being selected.

Categories:
(a) Type of wood used to make the cabinet: birch, maple, cherry.
     Each type of wood has a probability of 1/3 to be selected.
(b) Type of finish: transparent, semi-transparent.
    Each type of finish has a probability of 1/2 to be selected.
(c) Knob: bronze, steel, wood.
     Each material has 1/3 probability to be selected.

Each event (selecting material for the cabinet, for the finish, and for the knob) is an independent event.

Therefore
Probablity(birch wood AND bronze knob) = (1/3)*(1/3) = 1/9
Probability(wood knob) = 1/3
Probability(transparent stain) = 1/2
Probability(cheryy wood AND semi-transparent stain) = (1/3)*(1/2) = 1/6