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 ID: 680196
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Slide1
Independent vs Dependent Compound Probabilityand Tree DiagramsSlide2
Compound Probability – more than one event occursIndependent 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.Slide3
Independent EventsExample: 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.
Slide4
Dependent EventsExample: 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.
Slide5
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 ChocolateStrawberry cherry nuts Butterscotch
cherry
Slide6
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.Slide7
This is independent probability since flipping a coin does not affect using the spinner.
P(H, factor of 6) =
•
=
• = P(T, composite #) = • = Slide8
You have 2 red,
3 blue, 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.Slide9
You have 2 red,
3 blue, and 5 green marblesYou pick a marble, do not replace it, thenPick 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.
Slide10
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 PepperoniThick Mushroom Parmesan Pepperoni