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COMEDK · Maths · 36. Probability

Three fair dice are thrown. What is the probability of getting a total of 15 given that they exhibit three different numbers that are in arithmetic progression?

  1. A \(\dfrac{1}{4}\)
  2. B \(\dfrac{1}{2}\)
  3. C \(\dfrac{1}{6}\)
  4. D \(\dfrac{1}{8}\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(\dfrac{1}{6}\)

Step-by-step Solution

Detailed explanation

Let the three numbers on the dice be \(x, y, z\). The condition is that \(x, y, z\) are in arithmetic progression and are distinct. Let the numbers be \(a-d, a, a+d\) where \(d > 0\). Since the numbers are between \(1\) and \(6\), we have \(1 \le a-d\) and \(a+d \le 6\). For…