Question
Homework 4 Due: Wednesday, October 4, at the time when class is dismissnd Instructions This assignment has five problems. If your work is on suituple pleces of pape must staple all pieces togethes. If you don't showe al illegible, you may lose points. You must pus our solutions for problems in (incressingl orden I. Suppose you are the head of a laboratory that tests fot a cetain rare condition. Your test is pretty good: eiven that a patient actually has the condition, the patient will (correctly) teet pusitive 99% of the time! Therg are also very few false negatives: given that a patient does not live the condition, they will (corroctly) test negative8%%of the time However, the condition is very rare only .1% of all people have this condition. So, given that someune tests positive, what is the probability that they actually have the oondition? Suppose you are taking an exam that adjusts its difficulty on later questions based onl how well yoa do on previous questions. This exazn has only two peoblems. The first problem is mediur difficulty you think you have only a 65% chance of answering it correctly. If you get the first problem correct. then it nsks a more difficult qu stion that voi have a 40% chance of answering correctly. On the other hand, if you answer the first question incorroesly, then it will ask an easier question that yoa have a 85% chance of answering correctly. What is the probability that you aniswer the second question correctly? 3. You know that 30% of students in a certain clas have (ats, while 70% of students in the same class hav e dogs. If the events of having a dog and having a cat are independent for students in this class, then what percentage of students have both a cat and a dog? 4. In a previous class, 25% of students were sophomons. You know that 25% of spbonins got an A, and only 15% of nonsphoniores got azi A. What ierrentage of stirints who got in A were sophomores? 5. Suppose I have two events, A and B. If P(A)0 and P(B) >0, prove that A and B cannot be your choice), and then show that they cannot be the other int and independent. Hint: assume they are one of them (cither disjoint or independent,
Explanation / Answer
Sorry the writing is hazy. I suppose you are referring to Q4, here' your answer.
3.P(students have cat) = .30
P(students have dogs) = .70
Since having a dog and a cat are independent of each other we can say that P(A and B) = P(A)*P(B). or in other words:
P( student having a dog and a cat)
= P( having a dog )*P(having a cat)
= .30*.70
= .21
