Question

audrey has a box that contains one caramel chocolate (c), one milk chocolate (m), one dark chocolate (d), and one white chocolate (w). she picks one chocolate and eats it. then she picks another chocolate and eats it. what is the sample space of the event?

a. {m - d, m - w, m - c, d - w, d - c, w - c}
b. {m - d, m - w, m - c, d - m, d - c, d - w, w - m, w - c, w - d, c - m, c - d, c - w}
c. {m - d, m - w, m - m, d - m, d - c, d - d, w - m, w - w, w - d, c - m, c - d, c - c}
d. {m - d, m - w, m - c, m - m, d - m, d - c, d - w, d - d, w - m, w - c, w - d, w - w, c - m, c - d, c - w, c - c}

Explanation:

Step1: Understand sample - space concept

The sample space is the set of all possible outcomes.

Step2: List first - pick possibilities

If the first pick is M, the second can be D, W, or C. So we have M - D, M - W, M - C.

Step3: List first - pick as D possibilities

If the first pick is D, the second can be M, C, or W. So we have D - M, D - C, D - W.

Step4: List first - pick as W possibilities

If the first pick is W, the second can be M, C, or D. So we have W - M, W - C, W - D.

Step5: List first - pick as C possibilities

If the first pick is C, the second can be M, D, or W. So we have C - M, C - D, C - W.

Step6: Combine all outcomes

Combining gives {M - D, M - W, M - C, D - M, D - C, D - W, W - M, W - C, W - D, C - M, C - D, C - W}.

Answer:

B. {M - D, M - W, M - C, D - M, D - C, D - W, W - M, W - C, W - D, C - M, C - D, C - W}