Writing Exercise: Three people playing
mini-golf / 20%, 25%, and 30% chance of
each getting a hole-in-one
a) What are the chances of all 3 NOT
getting a hole-in-one
The tree above is INCORRECT because
remember that from each node, the
branches that come out of that node
represent a DECISION
--and all of the branches chances have to
ADD to 100%
We found the chances of arriving at each
of the leaf nodes we want... we then have
to ADD them because we are willing to
accept ANY of the three leaf nodes
(0.035 + 0.045 + 0.06) = 0.14
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Independent / Dependent Events
Example: You have a bag of blue and red
marbles (3 blue and 4 red)
You pick a marble, return it to the bag,
and then pick a second marble
What are the chances of picking Blue
twice?
Consider the same question but this time
do NOT return the marble after the first
pick
Notice that the probabilities on the
SECOND level are different depending on
which PATH we took for the first level
When this happens, we say that the
second event is DEPENDENT on the first
(We call an event INDEPENDENT if its
chances are not altered by the previous
event)
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The Multiplication Rule revisited
For events A and B that are parts of
an experiment
P(A and B) = P(A) * P(B)
P(BLUE on first and BLUE on second)
= P(BLUE on first) * P(BLUE on second)
= (3/7) * (we don't know which to pick 2/6
or 3/6)
= (3/7) * (BLUE on second such that we
picked a BLUE on first)
= (3/7) * (2/6) = 6/42
P(A and B) = P(A) * P(B | A)
The chance of B "such that" A has
occurred
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