Sara is deciding on the kind and color of new countertops for her kitchen. Her choices are granite (G) or quartz (Q). The color choices are charcoal (C), white (W), or Sand (S). Which TWO statements are correct?
Responses
A {GC, GW, GS, QC, QW, QS} is the sample space.{GC, GW, GS, QC, QW, QS} is the sample space.
B Sara can choose from 5 combinations.Sara can choose from 5 combinations.
C Sara can choose from 6 combinations.Sara can choose from 6 combinations.
D {G, Q, C, W, S} is the sample space.{G, Q, C, W, S} is the sample space.
E {GQ, C, W, S} is the sample space{GQ, C, W, S} is the sample space
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A is correct: the sample space includes all possible combinations of type and color, so it is {GC, GW, GS, QC, QW, QS}.
B is incorrect: there are 6 possible combinations, not 5.
C is correct: Sara can choose from 6 combinations in total, as stated in A.
D is incorrect: this is the set of all possible options (type and color), but not the sample space.
E is incorrect: this set is missing some combinations, such as G+C or Q+S.
The correct statements are A and D.
A {GC, GW, GS, QC, QW, QS} is the sample space. This statement correctly lists all of the possible combinations of countertop type and color.
D {G, Q, C, W, S} is the sample space. This statement correctly lists all of the possible options for countertop type and color, including the individual choices of granite (G), quartz (Q), charcoal (C), white (W), and sand (S).
To determine which statements are correct, let's analyze the problem:
Sara can choose between two types of countertops (granite or quartz) and three colors (charcoal, white, or sand).
A - {GC, GW, GS, QC, QW, QS} is the sample space.
This statement is correct. The sample space represents all possible combinations of countertop type (G or Q) and color (C, W, or S).
B - Sara can choose from 5 combinations.
This statement is incorrect. Since Sara has two options for countertop type and three options for color, she has a total of 2 x 3 = 6 combinations to choose from.
C - Sara can choose from 6 combinations.
This statement is correct. As explained above, there are 6 possible combinations for Sara to choose from.
D - {G, Q, C, W, S} is the sample space.
This statement is incorrect. {G, Q, C, W, S} represents the set of individual options available (countertop type and colors), but not all the combinations.
E - {GQ, C, W, S} is the sample space.
This statement is incorrect. {GQ, C, W, S} represents a mix of countertop type and colors, but it does not cover all the possible combinations.
So, the correct statements are A and C.