High School

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Dennis is choosing a pair of socks and a pair of shoes. For the socks, he can choose from blue, red, and black, and for the shoes, he can choose from boots, sandals, and loafers. What is the sample space of one pair of socks and one pair of shoes?

A) {blue boots, blue sandals, blue loafers, red boots, red sandals, red loafers, black boots, black sandals, black loafers}
B) {blue, red, black, boots, sandals, loafers}
C) {blue, red, black, boots, sandals, loafers, blue boots, red boots, black boots, blue sandals, red sandals, black sandals, blue loafers, red loafers, black loafers}
D) {2 blue socks, 2 red socks, 2 black socks, 2 boots, 2 sandals, 2 loafers}

Answer :

The correct sample space for Dennis's choice of one pair of socks and one pair of shoes is option A, which lists all possible combinations of socks and shoes. Therefore, the correct option is A

The question is regarding the calculation of a sample space for combining one pair of socks with one pair of shoes. Dennis has three choices for socks (blue, red, and black) and three choices for shoes (boots, sandals, and loafers). The sample space represents all possible combinations of one pair of socks with one pair of shoes. The correct sample space, which is composed of all possible outcomes, is given by the set:

{blue boots, blue sandals, blue loafers, red boots, red sandals, red loafers, black boots, black sandals, black loafers}

Therefore, the correct answer is A.

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