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