1. Compound Events – Independent and Dependent
Chp. 8 Sec 2-B pg

2. Compound Events Compound Events – two or more simple events
Example: Rolling a number cube and flipping a coin.
Independent Events – Events where the outcome of one does not affect the outcome of the other event. The above example is an independent event.
Dependent Event – Events where the outcome of one event affects the outcome of another event.
Example: A bag has 4 blue and 3 red marbles. You draw one marble out. WITHOUT REPLACING IT, you draw out a second marble. This is dependent because the first event “affects” the second event.

3. Compound Event We have a cup with 5 cubes in it, 4 red and 1 green.
We draw one cube out, replace it and then draw a second cube.
Is this an independent or dependent event?
Independent – the first event does not affect the second event
How about if you draw one cube out, DO NOT REPLACE and draw a second cube? Is it independent or dependent?
Dependent

4. Compound Event Probability - Independent
The probability of independent events is calculated by multiplying the probabilities together. P(A and B) = P(A) • P(B)
We have a cup with 5 cubes in it, 4 red and 1 green.
We draw one cube out, replace it and then draw a second cube.
1st cube is red.
P(A) = = 0.8 = 80%
2nd cube is green.
P(B) = = 0.2 = 20%
P(A and B) = P(A) • P(B)
P(A and B) = (0.8)(0.2) = 0.16 = 16%

5. Compound Event Probability - Dependent
The probability of dependent events is calculated by multiplying the probability of A and then the probability of B after A occurs P(A then B) = P(A) • P(B following A)
We have a cup with 5 cubes in it, 4 red and 1 green.
We draw one cube out, do not replace it and then draw a second cube.
1st cube is red.
P(A) = = 0.8 = 80%
2nd cube is green.
P(B) = = 0.25 = 25%
P(A then B) = (0.8)(0.25) = 0.2 = 20%