Section 9.4: Applications & Review

This section applies probability and combinatorics concepts to real-world problems and provides a review of key rules and methods.

Example 1: Probability in Real Life

A box has 5 red balls and 3 blue balls. Two balls are drawn without replacement. What is the probability both are red?

Step 1: First red ball: 5/8

Step 2: Second red ball: 4/7

Step 3: Multiply probabilities: 5/8 × 4/7 = 20/56 = 5/14

Example 2: Counting Outcomes

How many 4-letter “words” can be formed from the letters A, B, C, D, E without repetition?

Step 1: 1st letter: 5 choices

Step 2: 2nd letter: 4 choices

Step 3: 3rd letter: 3 choices

Step 4: 4th letter: 2 choices

Total arrangements: 5×4×3×2 = 120

Practice Problems

  1. A deck has 52 cards. Probability of drawing two aces in a row without replacement?
  2. From 6 boys and 4 girls, choose a committee of 3. How many ways?
  3. Probability of flipping 4 coins and getting exactly 2 heads?
  4. A bag contains 10 marbles: 4 red, 3 blue, 3 green. Draw one marble. Probability it is not green?
  5. From 5 different books, how many ways can 3 be arranged on a shelf?
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