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15 October, 10:47

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 HE, and that 10% of the ticks that had either Lyme disease or HGE carried both diseases. (a) What is the probability that a tick carries both Lyme disease (L) and HE (H) ? (b) What is the conditional probability that a tick has HE given that it has Lyme disease?

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  1. 15 October, 10:59
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    a) 0.024

    b) 0.148

    Explanation:

    Let 's represent the set of deer ticks Carrying Lyme disease with L and the set of deer ticks carrying Human Granulocytic Ehrlichiosis with H

    Given:

    P (L) = 0.16

    P (H) = 0.10

    P (L n H) = 0.1 ·P (L u H)

    Hence, P (L u H) = 10 ·P (L nH)

    (a)

    Hence. using the equation. P (L U H) = P (L) + P (H) - P (L n H)

    Hence, 10 · P (L n H) = 0.16 + 0.1 - P (L n H)

    Hence, 11 · P (L n H) = 0.16 + 0.1 = 0.26

    Hence, P (L n H) = 0.26/11=0.024

    (b)

    We know that condition probability P (H ║ L) = p (L n H) / P (L)

    hence, P (H ║ L) = (0.26/11) / 0.16 = 0.148
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