Deer ticks can be carriers of either Lyme disease or human granulocytic ehrlichiosis (HGE). Based on a recent study, suppose that 14% of all ticks in a certain location carry Lyme disease, 6% carry HGE, and 6% of the ticks that carry at least one of these diseases in fact carry both of them. If a randomly selected tick is found to have carried HGE, what is the probability that the selected tick is also a carrier of Lyme disease? (Round your answer to four decimal places.)

Deer ticks can carry both Lyme disease and human granulocytic ehrlichiosis (HGE). In a study of ticks in the Midwest, it was found that 15 % carried Lyme disease, while 11 % carried HGE. In addition, of the ticks with either Lyme disease or HGE, 16 % carried both diseases. (a) What is the probability P[L H] that a tick carrries both Lyme disease (L) and HGE (H)? P[LH] = (b) What is the conditional probability that a tick carries HGE, given that it has Lyme disease? P[H|L] =

An opinion poll asks a simple random sample of 500 adults whether they favor giving parents of school-age children vouchers that can be exchanged for education at any public or private school of their choice.  Each school would be paid by the government on the basis of how many vouchers it collected.  Suppose that in fact 47% of the population favor this idea. What is the probability that more than half (50%) of the sample are in favor?  (Use State/Plan/Do/Conclude)

A certain blood test is 99.5% effective at detecting Foreign Bloodborne Pathogens (such as the hepatitis virus) in human blood. If two people who take this test are selected at random, what is the probability both tests correctly detect a Foreign Bloodborne Pathogen? If ten people who take this test are selected at random, what is the probability all tests correctly detect a Foreign Bloodborne Pathogen? If 1,000 people who take this test are selected at random, what is the probability at least one test FAILS to detect a Foreign Bloodborne Pathogen?

The vast majority of European vehicles sold in the world (BMW, Audi, Mercedes- Benz, etc...) receive their transmissions from either ZF Friedrichshafen AG or Continental AG. After the acquisition of TRW by ZF, ZF AG supplied 69% of transmissions, and Continental AG supplied 31%. If three European cars are randomly selected, what is the probability that 2 of the cars use ZF transmissions and 1 use Continental AG transmission? Enter your answer in percent terms (for example 12.5% must be entered as 12.5).

According to the Center for Disease Control and Prevention (CDC), up to 20% of Americans contract the influenza virus each year, and approximately 3% of all births in the United States result in birth defects each year.  Consider two randomly selected Americans and assume that these two randomly selected Americans are independent of each other.  The probability that neither of these two randomly selected Americans will contract the influenza virus in a given year is

With regards to a particular gene, the percentage of genotypes AA, Aa, and aa in a particular population are respectively, 60%, 30%, and 10%. Furthermore, the percentages of these genotypes that contract a certain disease are respectively. 1%, 5% and 20%. If a person does contract the disease, what is the probability that the person is of genotype AA?

A particular automatic sprinkler system has two different types of activation devices for each sprinkler head. One type has a reliability of 0.75; that is, the probability that it will activate the sprinkler when it should is 0.75. The other type, which operates independently of the first type, has a reliability of 0.85. If either device is triggered, the sprinkler will activate. Suppose a fire starts near a sprinkler head. (provide your answer in four decimal numbers) (i) What is the probability that the sprinkler head will be activated? (1.5) (ii) What is the probability that the sprinkler head will not be activated? (1.5) (iii) What is the probability that both activation devices will work properly? (1.5) (iv) What is the probability that only the device with reliability 0.75 will work properly? (1.5)

A manufacturer wishes to estimate the accuracy of its final visual inspection process. A random sample of 180 devices is selected from production. An item is defective or “bad” if it contains at least one visually noticeable cosmetic defect.  The process improvement team agrees that the sample contains 27 bad items and 153 good items.  The team gives the items to a “certified” operator for inspection.  The operator rejects 10 good pieces and accepts 11 bad pieces and classifies the remainder correctly.  What is the probability that the inspector will reject an item?   P(inspector will reject an item) = ________%.  Enter value using one decimal place.