In a game where you roll two fair six-sided dice, what is the probability of rolling a sum that is a prime number?

Official Answer

Certainly, I'd be delighted to delve into this probability question. The essence of solving problems like these, especially from a Data Scientist's perspective, involves not just the application of statistical knowledge but also a creative approach to problem-solving and data interpretation.

To begin, let's break down the problem into manageable components. We're dealing with two fair six-sided dice, which means each die has an equal chance of landing on a number between 1 and 6. The task at hand is to determine the probability of the sum of these two dice being a prime number. Prime numbers in the context of the possible outcomes (2 through 12) are 2, 3, 5, 7, and 11.

Now, we systematically approach this by enumerating the possible outcomes that yield these prime sums. It's a method that mirrors how I tackle data analysis problems—breaking down complex data into understandable and actionable insights.

For a sum of 2, there's only 1 outcome: (1,1).
For a sum of 3, there are 2 outcomes: (1,2) and (2,1).
For a sum of 5, there are 4 outcomes: (1,4), (2,3), (3,2), and (4,1).
For a sum of 7, there are 6 outcomes: (1,6), (2,5), (3,4), (4,3), (5,2), and (6,1).
For a sum of 11, there are 2 outcomes: (5,6) and (6,5).

Adding these outcomes together gives us a total of 15 favorable outcomes that result in the sum being a prime number.

To find the probability, we also need to consider the total number of possible outcomes when rolling two dice. Since each die has 6 faces, the total number of combinations is 6 * 6 = 36.

The probability, therefore, of rolling a sum that is a prime number is the number of favorable outcomes (15) divided by the total number of outcomes (36). This simplifies to 15/36, which can be further reduced to 5/12.

In essence, the probability of rolling a sum that is a prime number with two six-sided dice is 5/12. This approach, breaking down the problem and methodically analyzing the components, is reflective of the analytical mindset I bring to the table. It's about dissecting data or a problem, understanding its components, and synthesizing the findings into actionable insights. For potential employers, this demonstrates not just theoretical knowledge, but a practical, applied capability to solve complex problems, a skill that's invaluable across data-centric roles.