Dependent and Independent Events

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Dependent and Independent Events
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If you have events that occur together or in a
row, they are considered to be compound events
(involve two or more separate events)
If the occurrence of one event has nothing to do
with the other, the events are considered to be
INDEPENDENT.
Ex. What is the probability of drawing a red card
from a full deck of card? What is the probability
of drawing a red card again if the first card was
placed back in the deck?
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What is the probability of turning five red cards
in a row?
Example What is the probability of flipping a
coin and rolling a three on a die?
½ x 1/6 according to our theory.
Therefore we know that P(A and B) P(A) x P(B)
for events that are independent.
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Example The probability that it is going to be
sunny is 0.4 when walking to school. The
probability of meeting up with your friend on the
way to school is 0.3. a) What is the prob of it
being sunny and walking to school with your
friend? b) What is the prob of it not being sunny
and walking to school with your friend? c) What
are the odds of it being sunny and walking to
school without your friend?
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In some cases, something will have to happen
first before something else can happen. For
example, If the outcome of an event directly
depends on the outcome of another event, they are
said to be dependent. This becomes conditional
probability.
If the outcome of B is dependent of the outcome
of A, then the cond. Prob. of B, P(BA), is the
probability that B occurs, given that A has
already occurred.
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Ex. In order to match up socks in a drawer, there
are 4 black socks, 6 red socks and 2 blue socks.
What is the probability that two black socks will
be chosen out of the drawer?
In this question there are 12 socks in total. We
want to choose 1 black sock first out of a total
of 4 black socks, therefore our probability of
choosing a black sock is 4/12.
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To choose the second black sock, we now have 11
socks to choose from and only 3 black chances,
therefore our probability of choosing a black
sock is 3/11.
Our total probability is calculated to be 4/12 x
3/11 1/11 or 0.09 9 chance
In that example, when two events are dependent we
still multiply the probabilities together,
however we must use the conditional prob for the
second event. Product rule for dependent
events. P(A and B) P(A) x P(BA)
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Remember that we can use this as a formula. If
we know the first and second items, we can easily
get the third item in the equation!
Homework Pg 334 1, 2,3,6,9,10, 17 try it