Unit 1: Probability and Set Theory

Unit 1: Probability and Set Theory Independent and Dependent Events

M8D3A ~ Students will find the probability of simple independent events. M8D3B ~ Students will find the probability of compound independent events.

When and why do I use addition to determine probabilities? When and why do I use multiplication to determine probabilities? How can I use probability to determine if a game is fair or to figure my chances of winning the lottery?

Compound Events are two or more events that can happen either at the same time or one after the other.

There are two types of compound events:

Independent Events ~ if the occurance of one event does not affect the likelihood that the other event will occur. P(A and B) = P(A)  P(B)

Dependent Events ~ if the occurance of one event does affect the likelihood that the other event will occur. P(A and B) = P(A)  P(B given A)

Examples: Tell whether the events are independent or dependent.

1. You roll a number cube. Then you roll the number cube again. 2. You randomly draw a number from a bag. Then you randomly draw a second number without putting the first number back. Examples: Tell whether the events are independent or dependent. Then find the probability.

3. You roll a number cube and get a 5. Then you roll the number cube a second time and get a 5 again.

4. A container has 7 green buttons, 3 yellow buttons, and 4 blue buttons. You reach in and randomly draw out a blue button. Without replacing the blue button, you reach in again and randomly draw out a second blue button.

5. You spin a penny and a nickel on a table. The penny lands heads up and the nickle lands tails up.

6. You are playing the bingo card B I N G O show. The caller has 50 12 18 41 51 66 numbers left to call. What is 7 26 44 54 70 the probability that you will 6 27 FREE 58 63 get bingo with the next 2 numbers 5 23 39 52 73 called? 3 30 36 57 75