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KATRIN_1
2 months ago
10

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 _____.
Mathematics
1 answer:
PIT_PIT [12.4K]2 months ago
6 0
Assuming that every material in their respective categories has an equal likelihood of selection.

Categories:
(a) Wood types for cabinets: birch, maple, cherry.
Each wood type has a selection probability of 1/3.
(b) Finish types: transparent, semi-transparent.
Each finish type has a 1/2 chance of being selected.
(c) Knob types: bronze, steel, wood.
Each knob material carries a probability of 1/3.

The selection of materials for the cabinet, finish, and knobs is independent of one another.

Consequently,
Probability(birch wood AND bronze knob) = (1/3)*(1/3) = 1/9
Probability(wood knob) = 1/3
Probability(transparent stain) = 1/2
Probability(cherry wood AND semi-transparent stain) = (1/3)*(1/2) = 1/6



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