Question

describe the sample space of possible outcomes.

determining a persons favorite steak (rib-eye (r), filet (f), t-bone (t), sirloin (s)) and doneness (rare (r), medium (m), well done (w))

choose the correct answer below.

a. \\{rr, rm, rw, fr, fm, fw, tr, tm, tw\\}
b. \\{rr, rm, fr, fm, tr, tm, sr, sm, rr, rm\\}
c. \\{rr, rm, rw, fr, fm, fw, tr, tm, tw, sr, sm, sw\\}
d. \\{rr, rm, fr, fm, tr, tm, sr, sm\\}

Explanation:

🆕 New Concept Discovered: Sample Space
All possible outcomes of an experiment

Step 1: Identify the components of each outcome

An outcome consists of two choices made together:

1. Favorite steak: Rib-eye (R), Filet (F), T-bone (T), or Sirloin (S)
2. Doneness: Rare (R), Medium (M), or Well done (W)

Step 2: List all possible combinations

To find the complete sample space, we pair each steak type with each doneness level:

• Rib-eye (R): RR, RM, RW
• Filet (F): FR, FM, FW
• T-bone (T): TR, TM, TW
• Sirloin (S): SR, SM, SW

Combining these gives a total of \(4 \times 3 = 12\) possible outcomes:

$$ \{RR, RM, RW, FR, FM, FW, TR, TM, TW, SR, SM, SW\} $$

Step 3: Match with the given options

• Option A is missing the Sirloin (S) combinations.
• Option B is missing the Well done (W) combinations and contains duplicates.
• Option C contains all 12 unique combinations.
• Option D is missing the Well done (W) combinations.

Answer:

C. {RR, RM, RW, FR, FM, FW, TR, TM, TW, SR, SM, SW}