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Warm - Up • 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?
Homework Answers #23-29 23. .308 24. A. .0800 B. .174 C. .054 D. .692 25. .8 26. yes, independent 28. A. 15% B. 20% 29. B. 30% C. 40%
Conditional Probability • 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:
The following is a two-way table of all suicides committed in a recent year by sex of the victim and method used:
What is the probability that a randomly selected suicide victim is male? • What is the probability that the suicide victim used a firearm? • What is the conditional probability that a suicide used a firearm, given that it was a man? A woman? • 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: • Here P(B|A) is the conditional probability that B occurs, given the information A occurs.
Example • 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?
Independent Events • Two events A and B that both have positive probability are independent if
Cautions • 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.
