Deca-Die I

Expected value of a sum from multiple independent dice rolls

This is a foundational probability question that tests your ability to compute expected values for sums of independent random variables. It rewards clean reasoning about linearity of expectation and understanding the mechanics of discrete uniform distributions.

To solve problems in this category, candidates typically identify the expected value of a single die, then use the fact that expectation is linear to extend that to multiple independent rolls. The key insight is that you do not need to enumerate all possible outcomes—structure and a simple principle do the work.

• Linearity of expectation
• Expected value of a uniform discrete distribution
• Sums of independent random variables