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Libniz
Group Title
Deer ticks can carry both Lyme disease and human
granulocytic ehrlichiosis (HGE). In a study
of ticks in the Midwest, it was found that 16% carried
Lyme disease, 10% had HGE, and that 10%
of the ticks that had either Lyme disease or HGE
carried both diseases.
(a) What is the probability PLH that a tick carries
both Lyme disease (L) and HGE (H)?
(b) What is the conditional probability that a tick
has HGE given that it has Lyme disease?
 one year ago
 one year ago
Libniz Group Title
Deer ticks can carry both Lyme disease and human granulocytic ehrlichiosis (HGE). In a study of ticks in the Midwest, it was found that 16% carried Lyme disease, 10% had HGE, and that 10% of the ticks that had either Lyme disease or HGE carried both diseases. (a) What is the probability PLH that a tick carries both Lyme disease (L) and HGE (H)? (b) What is the conditional probability that a tick has HGE given that it has Lyme disease?
 one year ago
 one year ago

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mathmate Group TitleBest ResponseYou've already chosen the best response.3
Let L=event of carrying Lyme's H=event of carrying HGE Then \( P(L\cup H) = P(L) + P(H)  P(L\cap H) \) But we also know that \( P(L \cap H) = 0.1P(L\cup H)\) So, substituting, \( 10P(L\cap H) = P(L) + P(H)  P(L\cap H) \) giving \( P(L\cap H) = \frac{(P(L) + P(H)) }{11} \) and \( P(HL) = \frac{P(H\cap L)}{P(L)} \)
 one year ago

mathmate Group TitleBest ResponseYou've already chosen the best response.3
You're welcome! :)
 one year ago

Libniz Group TitleBest ResponseYou've already chosen the best response.0
I believe it was a typo? \[P(L\cap H) = \frac{(P(L) + P(H)) }{10}\]
 one year ago

mathmate Group TitleBest ResponseYou've already chosen the best response.3
It comes from: \( P(L\cap H)=0.1P(L\cup H) \) or \( 10P(L\cap H)=(L\cup H) \) So \( 10 P(L∩H)=P(L)+P(H)−P(L∩H) \) If we transpose \( P(L\cap H) \) to the left, we get \( 11P(L∩H)=P(L)+P(H) \) and the rest follows.
 one year ago

Libniz Group TitleBest ResponseYou've already chosen the best response.0
Thank again
 one year ago

mathmate Group TitleBest ResponseYou've already chosen the best response.3
You're welcome!
 one year ago
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