Three ordinary dice are rolled. What is the probability that the results are all less than 5

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Three ordinary dice are rolled. What is the probability that the results are all less than 5

Calculate individual die probabilities:

• Die 1 P(x < 5) = 4/6 = 2/3
• Die 2 P(x < 5) = 4/6 = 2/3
  
• Die 3 P(x < 5) = 4/6 = 2/3

Since each roll is independent, we have:
P(Die 1 < 5, Die 2 < 5, Die 3 < 5) = 2/3 * 2/3 * 2/3
P(Die 1 < 5, Die 2 < 5, Die 3 < 5) = 8/27