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?

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