Probability

Vocabulary Outcome: any of the possible results of an action Example: 1 Sample Space: Set of all possible outcomes Example: 1,2,3,4,5,or 6

Example Create a tree diagram for rolling the dice. Dice 1 2 3 4 5 6

Example Create a tree diagram for the spinner

Probability of Simple Events Probability: chance that some event will occur Example: rolling a 6 Simple Event: one outcome or collection of outcomes

Example What is the probability of getting a red hat? 1 red hat out of 4 hats ¼ 0.25 25%

Example What is the probability of rolling a 6 on the dice?

Theoretical vs. Experimental Theoretical Probability Experimental Probability What should happen when conducting an experiment What actually happens when conducting an experiment

If you flip a coin ten times what is the theoretical probability of getting heads? Desired Outcome 1 Sample Space 2 1 X 2 10 You should get heads 5 times out of the ten tries. Step 1 Step 2: set up proportion Step 3: Cross Multiply

Example If you spin this spinner 20 times, what is the theoretical probability of getting green?

Example If you have a coin and flip it 20 times what is the probability of getting heads?

Independent Vs. Dependent Independent Probability Dependent Probability When one event does not affect the other event Example: When one event affects the other event Do Not Replace

Identify With Replacing Without Replacing Without Replacing

Example Independent A number cube is rolled and a marble is selected at random from the bag. Determine P(even and yellow). Step 1: determine the probability of each event. P(even) = 3/6 = ½ P(yellow) = 2/8 = ¼ Step 2: multiply P(even) X P(yellow) P(even and yellow) = ½ X ¼ P(even and yellow)= 1/8

Example Dependent Tina randomly selects a marble from the bag shown and then Nathan selects a marble randomly. What is the probability that both will get a green marble? Step 1: determine the probability of Tina choosing a green marble. P(Tina green) = 2/8 = ¼ Step 2: determine the probability of Nathan choosing a green marble also. P(Nathan green) = 1/7 Tina did not replace the green marble Step 3: Multiply P(Tina green) X P(Nathan green) P(both green) = ¼ X 1/7 P(both green)= 1/28