Math 141
Chapter 7 – 7.5, 7.6 Conditional Probability
TAMU – Summer 2014
Conditional Probability
Conditional Probability: If E and F are two events, then we say that the probability that E will occur
given that F occurs is P(E | F ), and is the “probability of E given F .”
P(E | F ) =
Example 1. P( E )= 0.3, P( F )= 0.7, P( E È F )= 0.2, find
a) P(EC| F )
b) P(E Ç F | F )
c) P(E | F C )
d) P(E È F C | F )
Example 2. A card is randomly selected from a deck of 52 cards. What is the probability that the card
selected is a King given that a card is higher than 10 and is black.
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Math 141
Chapter 7 – 7.5, 7.6 Conditional Probability
TAMU – Summer 2014
Example 3. Two bins contain transistors. The first bin has 10 defective and 20 non-defective
transistors. The second bin has 5 defective and 25 non-defective transistors, If the probability of
picking the first bin is twice the probability of picking the second bin, what is the probability (of )
a) picking a defective transistor, given it's picked from the first bin?
b) picking a good transistor and the second bin?
c) picking a defective transistor and the first bin?
d) that the defective transistor came from the second bin?
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Math 141
Chapter 7 – 7.5, 7.6 Conditional Probability
TAMU – Summer 2014
Example 4. Three machines turn out all the products in a factory, with the first machine producing 15%
of the products, the second machine 30%, and the third machine 55%. The first machine produces
defective products 11% of the time, the second machine 11% of the time and the third machine 8% of
the time. What is the probability that a non-defective product came from the second machine?
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Math 141
Chapter 7 – 7.5, 7.6 Conditional Probability
TAMU – Summer 2014
Independent Events : Events E and F are said to be independent if
P(E | F ) = P(E ) , P(F | E ) = P( F )
For independent events ,
P(E È F ) = P(E ) · P(F )
Example. A building has three elevators. The chance that elevator A is not working is 12%, the chance
that elevator B is not working is 15%, the chance that elevator C is not working is 9%. If these three
events are independent of each other, then what is the probability that
a) none of the elevators are working ?
b) exactly one of the elevators are not working ?
c) exactly one of the elevators IS working/
d) all the elevators are working?
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