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Section 7.5 – Conditional Probability
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Section 7.5
Conditional Probability
Example 1:
Two cards are drawn without replacement in succession from a wellshuffled
deck of 52 playing cards.
What is the probability that the second card drawn is an ace,
given that the first card drawn was an ace?
The previous example is an example of conditional probability.
Conditional Probability of an Event
If A and B
are events in an experiment and P(A)
≠
0, then the conditional probability that
the event B will occur given that the event A has already occurred is
)
(
)
(
)

(
A
P
B
A
P
A
B
P
I
=
Example 2:
Given P(E) = 0.26, P(F) = 0.58, and P(E
I
F) = 0.02.
Find P(EF).
Example 3:
Given P(E
U
F
c
)
c
= 0.37, P(F
c
) = 0.61 and P(E) = 0.27.
Find P(F
c
E
c
).
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Example 4:
A pair of fair dice is cast.
What is the probability that the sum of the
numbers falling uppermost is 6, if it is known that exactly one of the numbers is a 2?
Example 5:
A pair of fair dice is cast.
What is the probability that at least one of the
numbers falling uppermost is a 5, if it is known that the two numbers are different?
Example 6:
A box contains 4 red (numbered from 1 to 4) and 6 blue cards (numbered
from 5 to 10).
A card is chosen randomly.
a) What is the probability that the card is red?
b) What is the probability that the card is even numbered?
c) What is the probability that the card is red and even numbered?
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 Spring '08
 CONSTANTE
 Math, Conditional Probability, Probability

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