At an end-of-year party for the employees of a certain company, Martha has been given an opportunity to win as...

Phase 1: Owning the Dataset

Visualization

Let's create a 6×6 grid showing all possible outcomes:

Total possible outcomes: \(6 \times 6 = 36\)

Key Conditions

• Tablet Computer: Sum of two cards = 8
• Smartphone: At least one card shows 2

Phase 2: Understanding the Question

We need to find:

1. Probability of winning Tablet Computer
2. Probability of winning Both prizes

Phase 3: Finding the Answer

Part 1: Tablet Computer (Sum = 8)

Let's identify all pairs that sum to 8:

• (2,6): \(2 + 6 = 8\) ✓
• (3,5): \(3 + 5 = 8\) ✓
• (4,4): \(4 + 4 = 8\) ✓
• (5,3): \(5 + 3 = 8\) ✓
• (6,2): \(6 + 2 = 8\) ✓

That's 5 favorable outcomes out of 36 total.

Probability of Tablet = \(\frac{5}{36}\)

Part 2: Both Prizes

For both prizes, we need:

• Sum = 8 (for tablet) AND
• At least one 2 (for smartphone)

From our five pairs that sum to 8, which ones contain at least one 2?

• (2,6): Contains a 2 ✓
• (3,5): No 2
• (4,4): No 2
• (5,3): No 2
• (6,2): Contains a 2 ✓

Only 2 outcomes satisfy both conditions.

Probability of Both = \(\frac{2}{36} = \frac{1}{18}\)

Phase 4: Solution

Final Answer

• Tablet Computer: \(\frac{5}{36}\)
• Both prizes: \(\frac{1}{18}\)