Question

In a single throw of three dice, the probability of getting a sum of at least 5 is

• A. \( \frac{53}{54} \)
• B. \( \frac{51}{54} \)
• C. \( \frac{1}{54} \)
• D. \( \frac{2}{3} \)

Hint:

When calculating probability, always subtract the unfavorable outcomes from the total outcomes to find the favorable ones.

Answer 1

The Correct Option is A

Step 1: Total number of outcomes.
The total number of outcomes when rolling three dice is: \[ 6 \times 6 \times 6 = 216 \]
Step 2: Outcomes for sums less than 5.
The sums that are less than 5 are 3 and 4. For each sum, we count the possible combinations: - Sum of 3: Only \( (1, 1, 1) \), so 1 outcome. - Sum of 4: Possible combinations are \( (1, 1, 2), (1, 2, 1), (2, 1, 1) \), so 3 outcomes. Therefore, the total number of outcomes for sums less than 5 is \( 1 + 3 = 4 \).
Step 3: Calculating probability.
The number of favorable outcomes (sum at least 5) is \( 216 - 4 = 212 \). The probability is: \[ \frac{212}{216} = \frac{53}{54} \]
Step 4: Conclusion.
The correct answer is \( \frac{53}{54} \).