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.
B Sara can choose from 6 combinations.
C Sara can choose from 5 combinations.
D {G, Q, C, W, S} is the sample space.
E {GQ, C, W, S} is the sample space
A) {GC, GW, GS, QC, QW, QS} is the sample space.
B) Sara can choose from 6 combinations.
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You're welcome! Happy to assist! Don't hesitate to ask if you have any other questions.
To determine which of the statements are correct, let's break down the problem and calculate the sample space.
Sara has two choices for the kind of countertops, granite (G) or quartz (Q). She also has three choices for the color, charcoal (C), white (W), or sand (S).
To find the sample space, we multiply the number of choices for each category.
Number of choices for kind: 2 (G or Q)
Number of choices for color: 3 (C, W, or S)
To calculate the total number of combinations, we multiply the choices for kind and color:
Combinations = 2 (choices for kind) * 3 (choices for color) = 6
Now let's evaluate each statement:
A. {GC, GW, GS, QC, QW, QS} is the sample space.
The statement lists all 6 possible combinations, so statement A is correct.
B. Sara can choose from 6 combinations.
This statement correctly represents the total number of combinations, so statement B is correct.
C. Sara can choose from 5 combinations.
Since there are actually 6 combinations, statement C is incorrect.
D. {G, Q, C, W, S} is the sample space.
This statement lists all the options for kind and color, but it does not represent the combinations. Therefore, statement D is incorrect.
E. {GQ, C, W, S} is the sample space.
This statement does not represent the actual combinations of kind and color. It only includes one type of countertop, so statement E is incorrect.
Therefore, the correct statements are A and B.