Question

If four dice are thrown simultaneously, then the probability that none of the dice shows the number 1 on its face, is:

• A. \( \frac{625}{1296} \)
• B. \( \frac{125}{648} \)
• C. \( \frac{1250}{1296} \)
• D. \( \frac{625}{2592} \)

Hint:

When calculating probabilities with multiple events, multiply the individual probabilities together. Each die roll is an independent event.

Answer 1

The Correct Option is A

When a die is thrown, the total number of outcomes is 6. Since we want the dice not to show a 1, the remaining outcomes are 5, 2, 3, 4, 5, and 6 (so, 5 possible outcomes). For each die, the probability of not showing 1 is: \[ P(\text{not showing 1}) = \frac{5}{6} \] Since four dice are thrown simultaneously, the probability that none of the dice shows 1 on its face is: \[ P(\text{none of the dice shows 1}) = \left( \frac{5}{6} \right)^4 = \frac{625}{1296} \] Thus, the probability that none of the dice shows the number 1 is \( \frac{625}{1296} \).