Section 16.4.1 Probability Problems Solved with Combinations

1. Section 16.4.1 Probability Problems Solved with Combinations Pre-Calculus

2. Probability Solved with Combinations • This is just another method to help simplify calculating probabilities. • These problems can be solved in a multitude of ways. However, sometimes they can be quite tedious. • Thus, the combination method can be quite efficient and helpful.

3. Example 1 • Five cards are drawn at random from a standard deck. Find the probability that all 5 cards are hearts. • There are two methods to approach this. • Let’s take a look at the first method: • Method 1: • P(all hearts):

4. Method 2: Example 1 Continued • P(all hearts) = • out of the hearts choose 5 • out of all the cards choose 5 (sample space)

5. Summary

6. Example 2 • 5 cards are drawn at random from a standard deck. Find the probability that exactly 2 are hearts. • P(2 hearts, 3 non-hearts) • =

7. Example 3 • Thirteen cards are dealt from a well-shuffled standard deck. What is the probability that the 13 cards contain exactly 4 aces and exactly 3 kings? • P(13 cards with exactly 4 aces and exactly 3 kings) • =

8. Example 4 • Three marbles are picked at random from a bag containing 4 red marbles and 5 white marbles. What is the probability that • A) all 3 marbles are red • B) exactly 2 marbles are red

9. Example 4 Continued • Three marbles are picked at random from a bag containing 4 red marbles and 5 white marbles. What is the probability that • C) Exactly 1 marble is red • D) No marbles are red

10. Example 5 • Five cards are drawn at random from a standard deck. What is the probability of • A) all 4 aces are chosen • B) no aces are chosen • C) exactly 4 diamonds are chosen • D) four aces and one jack are chosen

11. Example 6 • Five cards are drawn at random from a standard deck. What is the probability of getting at least 1 ace?

12. Homework • Textbook pg 621: written exercises #1-3all