Mathematics
Mathematics
Problem
## QUICK REVIEW 9.9 (Prerequisite skill Section 9.3) Find the probability of each event: 1. Rolling a 6 on a single fair die 2. Rolling a total of 6 on a pair of fair dice 3. Drawing a 6 if we draw a single card from a deck of 52 cards 4. A 6 appearing as the first digit in a randomly generated set of five digits 5. A 6 appearing as the last digit in a randomly generated set of five digits 6. A 6 appearing as the first digit and the last digit in a randomly generated set of five digits. 7. A randomly generated set of five digits consisting of all 6's 8. A randomly generated set of five digits containing no 6's at all 9. A randomly generated set of five digits containing at least one 6 10. A randomly generated set of five digits containing at most one 6Intuitive explanation
Probability measures how likely an event is by comparing favorable outcomes to total possible outcomes. The key insight is recognizing what counts as a "favorable" outcome versus the full sample space—sometimes you'll count directly, sometimes you'll use complementary events (like finding "at least one" by subtracting "none" from the total). For multi-step or multi-digit scenarios, independence matters: if events don't affect each other, multiply their individual probabilities.
Intuitive explanation
Probability measures how likely an event is by comparing favorable outcomes to total possible outcomes. The key insight is recognizing what counts as a "favorable" outcome versus the full sample space—sometimes you'll count directly, sometimes you'll use complementary events (like finding "at least one" by subtracting "none" from the total). For multi-step or multi-digit scenarios, independence matters: if events don't affect each other, multiply their individual probabilities.