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Independent vs Dependent Compound Probability and Tree Diagrams

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.

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Independent vs Dependent Compound Probability and Tree Diagrams

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  1. Independent vs Dependent Compound Probabilityand Tree Diagrams

  2. 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.

  3. Independent Events • Example: You flip a coin, then roll the dice. P(H, composite #) = • = • = or 16.7 % P(T, not 4) = • = or 41.7% • Rolling the dice has no affect on flipping a coin.

  4. 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) = • = = or 16.7 % P(red, red) = • = = 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.

  5. 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 12 outcomes Chocolate cherry nuts Butterscotch cherry nuts Chocolate P(chocolate syrup ) = = Vanilla cherry nuts Butterscotch cherry nuts Chocolate Strawberry cherry nuts Butterscotch cherry

  6. Now you try: Flip a coin and spin the spinner. • Find P(H, factor of 6). • Find P(T, composite #). Ask yourself what kind of probability this is, then find the individual theoretical probabilities and multiply.

  7. This is independent probability since flipping a coin does not affect using the spinner. • P(H, factor of 6) = • = • = • P(T, composite #) = • =

  8. You have 2 red, 3blue, and 5 green marbles You pick a marble do not replace it, then pick another marble. • Find P(blue, green). • Find P(blue, blue). Ask yourself what kind of probability this is, then find the individual theoretical probabilities and multiply.

  9. You have 2 red, 3 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) = • = = This is dependent probability because what happens first affects your next pick. The denominator goes down by 1 and sometimes so does the numerator.

  10. 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

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