Deer ticks can carry both Lyme disease (L) and human granulocytic ehrlichiosis (H). In a study of ticks in the Midwest, it was found that 16% carried L, 10% carried H and 25% that had either L or H carried both. In other words, we know that
P(L) = 0.16, P(H) = 0.10, P(L H|L H) = 0.25.
The sample space of this problem is defined to be {NN, LN, NH, LH}, where NN denotes that a tick does not have L and H, LN denotes that a tick has L but not H, NH denotes that a tick has H but not L and LH denotes that a tick has both. Write down the set of outcomes in event L, i.e., a tick has L; and the set of outcomes in event H, i.e., a tick has H.
What is the probability that a tick carries both L and H, i.e., P(LH)?
What is the conditional probability that a tick has H given that it has L, i.e., P(H|L)?