Deer ticks can be carriers of either Lyme disease or human granulocytic ehrlichi

Question

Deer ticks can be carriers of either Lyme disease or human granulocytic ehrlichiosis (HGE). Based on a recent study, suppose that 14% of all ticks in a certain location carry Lyme disease, 6% carry HGE, and 6% 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? (Round your answer to four decimal places.) Deer ticks can be carriers of either Lyme disease or human granulocytic ehrlichiosis (HGE). Based on a recent study, suppose that 14% of all ticks in a certain location carry Lyme disease, 6% carry HGE, and 6% 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? (Round your answer to four decimal places.)

Explanation / Answer

Ans:

L=lyme,H=HGE

P(L)=0.14

P(H)=0.06

P(L and H/Lor H)=0.06

P(L and H)=0.06*(P(L or H)

P(L and H)=0.06*(P(L)+P(H)-P(L and H))

1.06*P(L and H)=0.06*(0.14+0.06)

P(L and H)=0.06*0.2/1.06=0.011321

Now,

P(L/H)=P(L and H)/P(H)=0.011321/0.06=0.1887

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