Question

a jewelry store sells gold, platinum and silver earrings. each is fitted with a diamond, sapphire or emerald. write out the sample space for this situation.

Explanation:

Step1: Identify categories

We have two categories: metal (gold, platinum, silver) and gem (diamond, sapphire, emerald).

Step2: List all combinations

For each metal, pair with each gem. So:

• Gold with diamond: (Gold, Diamond)
• Gold with sapphire: (Gold, Sapphire)
• Gold with emerald: (Gold, Emerald)
• Platinum with diamond: (Platinum, Diamond)
• Platinum with sapphire: (Platinum, Sapphire)
• Platinum with emerald: (Platinum, Emerald)
• Silver with diamond: (Silver, Diamond)
• Silver with sapphire: (Silver, Sapphire)
• Silver with emerald: (Silver, Emerald)

Answer:

The sample space is \(\{(Gold, Diamond), (Gold, Sapphire), (Gold, Emerald), (Platinum, Diamond), (Platinum, Sapphire), (Platinum, Emerald), (Silver, Diamond), (Silver, Sapphire), (Silver, Emerald)\}\)