1. Independent and Dependent Events Lesson 6.6

2. Getting Started… You roll one die and then flip one coin. What is the probability of : P(3, tails) = 2. P(less than 4, head) = 3. P(1, tails) = 4. P(even number, head) = 1/6 * ½ = 1/12 1/2 * ½ = 1/4 1/6 * ½ = 1/12 3/6 * ½ = 1/4

3. Definitions Probability of Independent Events: Events that do not change based on a previous performance. P(A and B) = P(A) * P(B) Examples: -Flipping a Coin 3 times -Rolling a Die 2 times -A spinner

4. Examples: A bag contains 12 marbles. There are 3 blue, 5 red, and 4 green. You draw one marble, replace it, and draw again. The probability that the first marble is blue and the second is green is: 3/12 * 4/12 = 12/144  1/12

5. Probability of Dependent Events: Events that are affected by events in the past. Examples: – Choosing 2 cards in a deck at random – Choosing a doughnut after 4 have already been taken from the box. P(A and B) = P(A) P(B| A)

6. 12 marbles - There are 3 blue, 5 red, and 4 green. Use the same bag of marbles Suppose you draw two marbles without replacement. The probability that the first marble is blue and the second is green is: 3/12 * 4/11 = 12/132  1/11

7. Mutually Exclusive Events If one event occurs, there is a 0% chance that another event will occur. Examples: That will be snowing and 75˚ outside When I roll my dice, I will get a sum of a 3 and an 8. P(A or B) = P(A) + P(B)

8. Examples: P(a sum of 2 or 8) = P(sum of 1 or 10) = + 5/36 = 6/36  1/61/36 + 3/36 = 3/36  1/120/36

9. You Try! Two Rolls of the Dice : P(3,3) Pick two cards from a deck: Both Hearts Roll two different dice: Sum is a 6 or a 12: 1/36 1/4 * 12/51 = 3/51 5/36 + 1/36 = 1/6