Two examples of probability and statistics problems include finding the probability of outcomes from a single dice roll and the mean of outcomes from a series of dice rolls. Finding the probability of outcomes from a single dice roll involves application of the Bernoulli distribution probability formulae, while finding the mean of a series of dice rolls is a basic statistical problem of evaluating the first moment of an event.

The most-basic example of a simple probability problem is the classic dice roll, which is a Bernoulli distribution problem. For example, if a dice is rolled, what is the probability that it lands on an even number? To answer this question, one first needs to count the possible number of even outcomes (which are three in total) and divide it by the number of possible roll outcomes (which are six in total). The probability is therefore a half.

The above scenario produces a statistical problem if the dice rolls seven times and creates a series of rolling events. From these events, seven different values emerge as outcomes e.g. 3, 2, 2, 5, 1, 6 and 4. Finding the mean of these outcomes is therefore a statistical problem. To find the mean of the seven dice rolls, sum up the values and divide them by the total number of rolls. Therefore the mean is equal to 23 divided by 7 which is 3.286.