Quiz 4

1. Quiz 4 Uncertainty & First Order Logic

2. 1) Joe is worried he has contracted measles. He goes to the doctor who tests his blood for measles. The test come back positive (virus detected). Joe asks the doctor what the accuracy of the test is. The doctor replies:”in 999 out of a 1000 patients who have measles the test came indeed out positive.” The doctor goes on to say, “But for people who don’t have measles, the test still came out positive in 1 out of 100 people”. Joe (now worried) looks up how many people actually have measles these days. He finds, 1 in 10,000 people have measles. Joe (who is very smart) does the following calculation: P(test=T) = P(test=T | measles=T) P(measles=T) + P(test=T | measles=F) P(measles=F). a) [2pts] Compute P(test=T) from the available information. b) [2pts] Use Bayes rule to express P( measles=T | test=T ) in terms of P(test=T | measles=T), P(measles=T) and P(test=T) and compute this probability form the available information. 2) Determine whether the following statements are valid (true in all worlds). x lives in some arbitrary domain. a) [2pts] b) [2pts]

3. 1) Joe is worried he has contracted measles. He goes to the doctor who tests his blood for measles. The test come back positive (virus detected). Joe asks the doctor what the accuracy of the test is. The doctor replies:”in 999 out of a 1000 patients who have measles the test came indeed out positive.” The doctor goes on to say, “But for people who din’t have measles, the test still came out positive in 1 out of 100 people. Joe (now worried) looks up how many people actually have measles these days. He finds, 1 in 10,000 people have measles. Joe (who is very smart) does the following calculation: P(test=T) = P(test=T | measles=T) P(measles=T) + P(test=T | measles=F) P(measles=F). a) [2pts] Compute P(test=T) from the available information. 999/1000 x 1/10000+1/100 x 9999/10000=0.0100989 b) [2pts] Use Bayes rule to express P( measles=T | test=T ) in terms of P(test=T | measles=T), P(measles=T) and P(test=T) and compute this probability form the available information. p(m|t)=p(t|m)xp(m)/p(t)  p(m=T|t=T)=999/1000x1/10000/ 0.01= 0.00989 2) Determine whether the following statements are valid (true in all worlds). x lives in some arbitrary domain. False a) [2pts] b) [2pts] True