• You have torn a tendon and are facing surgery to repair it. The
orthopedic surgeon explains the risks to you. Infection occurs in
3% of such operations, the repair fails in 14%, and both
infection and failure occur together in 1%. What percent of
these operations succeed and are free from infection?
23.
24.
25.
26.
28.
29.
.308
A. .0800
B. .174
.8
yes, independent
A. 15%
B. 20%
B. 30%
C. 40%
C. .054
D. .692
• Gives the probability of one event under the condition that we
know another event.
• The probability of B given A would be written as P(B|A)
• When P(A) > 0, the conditional probability of B given A is:
P  B | A 
P  A B
P  A
• The following is a two-way table of all suicides committed in a
recent year by sex of the victim and method used:
Male
Female
Firearms
15,802
2,367
Poison
3,262
2,233
Hanging
3,822
856
Other
1,571
571
Total
24,457
6,027
1. What is the probability that a randomly selected suicide victim
is male?
2. What is the probability that the suicide victim used a firearm?
3. What is the conditional probability that a suicide used a
firearm, given that it was a man? A woman?
4. What is the probability that the suicide victim was a woman,
given that she used poison?
• General Multiplication Rule for Any Two Events
• The joint probability that events A and B both happen can be
found by:
P  A B   P  A P  B | A 
• Here P(B|A) is the conditional probability that B occurs, given
the information A occurs.
• Functional Robotics Corporation buys electrical controllers from
a Japanese supplier. The company’s treasurer feels that there is
probability 0.4 that the dollar will fall in value against the
Japanese yen in the next month. The treasurer also believes that
if the dollar falls, there is a probability 0.8 that the supplier will
demand renegotiation of the contract. What probability has the
treasurer assigned to the event that the dollar falls and the
supplier demands renegotiation?
• Two events A and B that both have positive probability are
independent if
P B | A  P B
• It is easy to confuse probabilities and conditional probabilities
involving the same event.
• Be sure to keep in mind the distinct roles in P(B|A) of the event
B whose probability we are computing and the event A
represents the information we are given.