Mathematics
Mathematics
Problem
Two unbiased six–faced dice are thrown together once. Answer the following questions based on the experiment: a. (i) How many ordered pairs constitute the complete sample space? State the answer without listing all the pairs. b. (ii) Find the probability that the sum of the two numbers obtained is exactly 9. c. (iii) Find the probability that the sum of the two numbers obtained is at least 9.Intuitive explanation
When two dice roll together, you're really exploring compound probability — how individual independent events combine. The key insight is that the total number of equally likely outcomes is the product of outcomes from each die (36 total), and you count favorable outcomes by listing or organizing all the ways an event can happen. Think of it as filling a grid: each row is one die's result, each column is the other's, and you mark which cells match your condition.
Intuitive explanation
When two dice roll together, you're really exploring compound probability — how individual independent events combine. The key insight is that the total number of equally likely outcomes is the product of outcomes from each die (36 total), and you count favorable outcomes by listing or organizing all the ways an event can happen. Think of it as filling a grid: each row is one die's result, each column is the other's, and you mark which cells match your condition.