#### Transcript Independent vs Dependent Compound Probability and Tree

Independent vs Dependent Compound Probability and Tree Diagrams • Compound Probability – more than one event occurs • Independent events – one event is not affected by the outcome of the other event. • Dependent events – one event is affected by the outcome of the other event. You multiply the individual theoretical probabilities to get your answer. • Independent Events • Example: You flip a coin, then roll the dice. 𝟏 𝟐 P(H, composite #) = • P(T, not 4) = 𝟏 𝟐 • 𝟐 𝟔 𝟓 𝟔 = = 𝟏 𝟐 𝟓 𝟏𝟐 • 𝟏 𝟑 = 𝟏 𝟔 or 16.7 % or 41.7% • Rolling the dice has no affect on flipping a coin. • Dependent Events • Example: You pick a marble from a bag DO NOT REPLACE IT, then pick another marble. • You have 3 red, 2 blue, and 5 green marbles P(red, green) = 𝟑 𝟏𝟎 P(red, red) = • 𝟑 𝟏𝟎 𝟓 𝟗 = • 𝟐 𝟗 𝟏𝟓 𝟗𝟎 = = 𝟔 𝟗𝟎 𝟏 𝟔 = or 16.7 % 𝟏 𝟏𝟓 or 6.7% When you take one marble you have less marbles so your denominator goes down by one number. Your numerator may also be affected. • Tree diagrams – used to list possible outcomes then you can calculate individual probabilities. chocolate, vanilla, or strawberry ice cream, chocolate or butterscotch syrup and nuts or a cherry nuts Chocolate Chocolate 12 outcomes cherry nuts Butterscotch cherry nuts Chocolate Vanilla P(chocolate syrup ) = cherry nuts Butterscotch cherry nuts Chocolate Strawberry cherry nuts Butterscotch cherry 𝟔 𝟏𝟐 1 =2 • Now you try: Flip a coin and spin the spinner. 1) Find P(H, factor of 6). 2) Find P(T, composite #). Ask yourself what kind of probability this is, then find the individual theoretical probabilities and multiply. • This is independent probability since flipping a coin does not affect using the spinner. 1) P(H, factor of 6) = 1 2 2) P(T, composite #) = 1 2 • 4 8 • 3 8 = 1 2 = 3 16 • 1 2 = 1 4 • You have 2 red, blue, and 5 green marbles You pick a marble do not replace it, then pick another marble. 1) Find P(blue, green). 2) Find P(blue, blue). Ask yourself what kind of probability this is, then find the individual theoretical probabilities and multiply. • You have 2 red, blue, and 5 green marbles You pick a marble, do not replace it, then Pick another marble. 1) Find P(blue, green) = 2) Find P(blue, blue) = 3 10 3 10 • • 2 9 5 9 15 90 = = 6 1 = 90 15 = 1 6 This is dependent probability because what happens first affects your next pick. The denominator goes down by 1 and sometimes so does the numerator. You can choose from thin or thick crust pizza, mozzarella or parmesan cheese, and mushrooms or pepperoni. Draw a tree diagram. Mushroom 8 outcomes Mozzarella Pepperoni Thick P(mushroom) Mushroom Parmesan Pepperoni Mushroom Mozzarella Pepperoni Thick Mushroom Parmesan Pepperoni 𝟒 𝟔 = 𝟐 𝟑