What is the probability of getting a sum 8, while throwing two dice together?
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What is the probability of getting a sum 8, while throwing two dice together?
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Answer: D. 5/36
When rolling two dice, there are 36 total possible outcomes (6 × 6). The favorable outcomes that sum to 8 are: (2,6), (3,5), (4,4), (5,3), (6,2)—exactly 5 outcomes. Therefore, the probability is 5/36.
Step-by-step Derivation:
Step 1: Total possible outcomes when rolling two dice = 6 × 6 = 36.
Step 2: List all outcomes that sum to 8:
- Die 1 = 2, Die 2 = 6 → Sum = 8 ✓
- Die 1 = 3, Die 2 = 5 → Sum = 8 ✓
- Die 1 = 4, Die 2 = 4 → Sum = 8 ✓
- Die 1 = 5, Die 2 = 3 → Sum = 8 ✓
- Die 1 = 6, Die 2 = 2 → Sum = 8 ✓
Step 3: Favorable outcomes = 5.
Step 4: Probability = Favorable outcomes / Total outcomes = 5/36.
Note: Options A (1/5 ≈ 0.20), B (1/8 = 0.125), and C (1/9 ≈ 0.111) are all incorrect. The correct answer is D (5/36 ≈ 0.139).