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From the textbook: Probability and Statistics for Engineering and the Sciences (9th Edition) Deer ticks can...

From the textbook: Probability and Statistics for Engineering and the Sciences (9th Edition)

Deer ticks can be carriers of either Lyme disease or human granulocytic ehrlichiosis (HGE). Based on a recent study, suppose that 16% of all ticks in a certain location carry Lyme disease, 10% carry HGE, and 10% 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?

In chapter 2, problem 55e on step 3, why does A intersect B turn into a 1 so that 1 + 0.10 is multiplied by the second A intersect B?

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