Final answer:
To calculate the probability that all four outcomes are the same when rolling a fair six-sided die four times, we divide the number of favorable outcomes by the total number of outcomes. In this case, there is one favorable outcome for each possible outcome, resulting in a probability of 1/216.
Step-by-step explanation:
To find the probability that all four outcomes are the same when rolling a fair six-sided die four times, we need to consider the total number of outcomes and the number of favorable outcomes.
The total number of outcomes when rolling a six-sided die four times is 6 * 6 * 6 * 6 = 1296.
To calculate the number of favorable outcomes, we need to count the number of ways we can get the same outcome on all four rolls.
Since there are 6 possible outcomes on each roll, we have one favorable outcome for each outcome. Therefore, the number of favorable outcomes is 6.
The probability of all four outcomes being the same is the number of favorable outcomes divided by the total number of outcomes, i.e. 6/1296 = 1/216.