COMPOSITE EVENTS

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COMPOSITE EVENTS
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The probability that it rains is 70
The probability that it does NOT rain is
30
Instinct tells us that for any event E, the
probability that E happens the
probability that E does NOT happen 100
P(E) P(E) 100 100/100
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Flip 3 coins
2 x 2 x 2 8
possible outcomes
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Flip 3 coins
2 x 2 x 2 8 possible outcomes
NOT ALL TAILS
The probability that at least one lands heads up
7/8
ALL TAILS
The probability that all land tails up 1/8
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FLIP 10 COINS
What is the probability that at least one lands
heads up?

10 The number of possible outcomes
2 1024
P( all tails ) 1/1024
P( NOT all tails ) P(at least one heads up )
1023/1024
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Roll 4 dice
6 x 6 x 6 x 6
1296 possible outcomes
What is the probability that at least two land
on the same number?
Some of the possible outcomes 2 3 1 6 5 2 5 1 4
4 4 3 1 6 3 5 3 4 2 1 1 2 6 2 . .
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Roll 4 dice
It would be very difficult to count the number of
ways in which at least two land on the same
number.
Instead lets try to count the number of ways in
which it does NOT happen that at least two are
the same .. That is
They ALL land on DIFFERENT numbers
ways blue die can land 6
ways red die can land x 5
ways yellow die can land x 4
ways green die can land x 3
360
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Roll 4 dice
6 x 6 x 6 x 6
1296 possible outcomes
P( all different ) 360/1296
P( NOT all different ) 1 - 360/1296
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P( NOT all different ) 1 - 360/1296
1296/1296 - 360/1296
936/1296
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The probability that you get an A in French is
1/10
The probability that you get an B in French is
3/10
What is the probability that you get an A OR a
B in French?
Instinct tells us to add when we see the word
OR 1/10 3/10 4/10 P( A OR B )
In some cases, there is more to consider.
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shuffle this deck of 10 cards and draw one at
random. What is the probability that
it is a white card OR a King ?
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P ( white OR King ) 6/10
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P ( white OR King ) 6/10
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Draw 2 cards without replacement from a standard
deck of 52 cards.
What is the probability that both are red OR
both are kings?
P ( both red ) P( R ) 325/1326
P ( both kings ) P( K ) 6/1326
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P ( both red ) P( R ) 325/1326
P ( both kings ) P( K ) 6/1326
Both are red AND both are kings only 1 of the
1326 possible hands satisfies this condition
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P ( both red ) P( R ) 325/1326
P ( both kings ) P( K ) 6/1326
1/1326
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There are 10 women in a study.
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S
3 of them smoke
There are 10 women in a study.
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S
H
3 of them smoke
3 develop heart disease
There are 10 women in a study.
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S
H
The probability that a woman in this sample
develops heart disease P(H) 3/10
3 develop heart disease
There are 10 women in a study.
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H
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S
The probability that she gets heart disease IF
she smokes 2/3
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P(H) 3/10 30 P(H IF S) P(H/S) 2/3 66.7
Based on this data, we might conclude that a
woman is more than twice as likely to develop
heart disease IF she smokes.
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P(H IF S) P(H/S) 2/3 66.7
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P(H IF S) P(H/S) 2/3 66.7
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The probability that B happens IF A happens
the probability that A happens AND B
happens the probability that A
happens
We rewrite this formula to obtain a formula for
measuring the probability that A
happens AND B happens
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Multiply both sides of the equation by P(A)
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There is a 40 chance that my car wont start IF
it rains. There is a 70 chance of rain. What is
the probability that it rains AND my car wont
start.
(.40)
(.70)
.28
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P(both blue) P(first is blue AND second is blue)
A jar contains 2 red and 3 blue marbles. Draw
two without replacement. What is the
probability they are both blue?
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NOT OR IF AND