They are saying that out of 11 who test positive, only 1 is infected. Therefore the probability is 1/11 or 9%
Problem 10.
Construct a hypothetical table of 100,000 people. Of the 10,085 testing positive, 95/10085 = 0.0094 or .94% are sick.
Problem 12.
a) 0.925
b) 0.10
c) 0.107
Problem 13.
a) sensiivity is 0.80. Specificity is 0.90. These corespond to the proabilities of corectly testing positive and correctly testing negative.
Problem 15.
The proaility of someone having a particular birthday, namely that of the professor, is much smaller than the proability that there will be some date in common for some pair in class. He was probabily not successful, because the proability for each student would be only 1/365. On average, we could expect 50/365 matches or 0.14, which means that a match would occur in about 1 in 7 classes. the proability of no match would be (364/36)^50 = about 0.87.
Problem 16.
The sensitivity of 0.90 is the probability of a positive test when someone has the disease, so the probability of a negative test when someone actually has the disease, a false negative, is 0.10. We cannot find the probability of a false positive.
Problem 18.
There are numerous ways in which the statement could be true - the statement about the mother woud apply if she was deceased, if she lived in a distant city, if there was friction in the relationship, or if the person was not as close to her as desired.
Problem 21.
They are offering the equivalent deals interms of the average cost of each suit. the 50% off deal may be better because you only have to buy one suit to acheive the savings.
Problem 23.
There are two posillities. You pay 25 with probability 1/100 or pay nothing with probability 99/100 so the expected value is .25 or 25 cents. It will costan average of 25 cents each time you risk etting a ticket, which seems like a cheap price for parking.