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

speed of light in vacuum is 300,000 km/s

speed of light in other mediums is given by the expression v = c/n, where c is the speed of light in vacuum and n is the refractive index of medium.

for the first medium v = 200,000 km/s

  so, refractive index of medium = 300000/200000 = 1.5

    1.5 refractive index is usually for glass. so first medium is glass.

for the second medium v = 250,00 km/s

so, refractive index of medium = 300000/250000 = 1.2

    1.2 refractive index is usually for water. so second medium is water.

for the third medium v = 0 km/s

so, refractive index of medium = 300000/0 = ∞

    ∞ refractive index is usually for opaque mediums. so third medium is opaque medium.