math319_S10_Midterm

# math319_S10_Midterm - Math 319 Spring 2010 Midterm Thursday...

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Math 319, Spring 2010 Midterm Thursday, March 11, 2010 9.05 - 10.15 am Name : No use of notes or textbook - For full credit, show work and explain answers - Work alone 1. Consider an experiment whose sample space is S . For each event E of the sample space S , we assume that a number P ( E ) is defined and satisfies three axioms. State these three axioms. 2. Consider an experiment whose sample space is S . Assuming the Axioms you stated in Question 1, and that P ( ) = 0, prove each of the following. (a) For any finite sequence of mutually exclusive events E 1 , E 2 , . . . , E n , P n [ i =1 E i ! = n X i =1 P ( E i ) . 1

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(b) For any event E , P ( E c ) = 1 - P ( E ) . (c) For any events E 1 , E 2 , P ( E 1 E 2 ) = P ( E 1 ) + P ( E 2 ) - P ( E 1 E 2 ) . 2
3. (a) A patient arrives at a doctor’s office with a sore throat and low-grade fever. After an exam, the doctor decides that the patient has either a bacterial infection or a viral infection or both. The doctor decides that there is a probability of 0.7 that the patient has a bacterial infection and a probability of 0.4 that the person has a viral infection. What is the probability that the patient has both infections? Briefly

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