Lyme disease is one of the most common tick-transmitted diseases. Its tell-tale symptom is a bulls-eye shaped rash around the tick bite. Diagnosing Lyme disease in dogs is difficult because the bite area is covered by fur. A symptom of Lyme disease in dogs is lameness, but this is often mistaken for regular arthritis. At a veterinary hospital in Virginia, 120 lame dogs were tested for arthritis and Lyme disease. The results showed that 42 of the dogs had Lyme disease, and 96 had arthritis.

a. How many dogs had both Lyme disease and arthritis? Explain your reasoning. Fill in the Venn diagram with your results.

Dogs with Lyme disease Dogs with Arthritis

You want to complete a risk analysis for a dog chosen at random. Use the diagram to find each probability. Express each probability as a fraction and as a decimal.

b. P(Lyme disease) =
c. P(Arthritis) =
d. P(Lyme disease only) =
e. P(Arthritis only) =
f. P(Lyme disease or Arthritis) =
g. P(Lyme disease and Arthritis) =