Chapter 11 Probability and Tree Diagram

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Presentation transcript:

Chapter 11 Probability and Tree Diagram 1% of employees in a company are drug users. A test was developed to identify the drug users. If a person is a drug user, then the test returns positive result 98% of the time. If a person is not a drug user, the test returns negative result 97% of the time. Will you recommend this test to be administered at your company?

Conditional Probability and Tree Diagrams A package will be picked up by one of 3 delivery vans, depending on which is nearest. The choices are equal for any of the vans to make the pick up. Past record for each van’s success in delivering packages are given as follows: Prob(on time delivery for van 1) = .95 Prob(on time delivery for van 2) =.96 Prob(on time delivery for van 3) = .90. What is the probability a package will be delivered on time? ANS 0.94 Is package deliver independent of delivery van? NO If package is delivered on time, what is the probability that it was delivered by Van 1? ANS 0.338

Bayes’ Theorem-Reversing the Conditioning

At a gas station, 40% of customers pump regular gas, 35% pump midgrade gas, and 25% pump premium grade gas. Of those who pump regular, 30% pay at least $30. Of those who pump midgrade, 50% pay at least $30. And of those who pump premium, 60% pay at least $30. a) What is the probability that the next customer will pay more than $30? ANS 0.445 b) If the next customer pays more than $30, what is the probability that he pumped regular gas? ANS 0.269

Reversing the Condition A firm that specializes in filing out income tax forms has two types of accounts Large(gross income greater than $50000) Small(gross income less than $50000) They find that 5% of the large accounts and 2% of the small accounts are audited by the IRS. If 40% of their accounts are large accounts, and an account is audited, what is the probability that it is large? ANS 0.625