A single die is rolled three times. What is the probability that a 4 will show on the upward face at least once?

Sure, here's how you can calculate the probability:

Step 1: Understand the problem A die has 6 faces, numbered from 1 to 6. When you roll it, any number from 1 to 6 has an equal chance of showing up, which means the probability of getting any specific number, like 4, is 1/6.

Step 2: Calculate the probability of not getting a 4 The probability of not getting a 4 in a single roll is 5/6 (since 5 out of the 6 possible outcomes are not 4).

Step 3: Calculate the probability of not getting a 4 in three rolls Since each roll is independent, you can multiply the probabilities together to get the overall probability. So, the probability of not getting a 4 in three rolls is (5/6) * (5/6) * (5/6) = 125/216.

Step 4: Calculate the probability of getting a 4 at least once The probability of getting a 4 at least once is the opposite of not getting a 4 in all three rolls. So, you subtract the probability of not getting a 4 from 1 to get the probability of getting a 4 at least once. So, the probability is 1 - 125/216 = 91/216.

So, the probability that a 4 will show on the upward face at least once when a die is rolled three times is 91/216.