Probability Theory - conditional

[FrogPad]

Question:
Deer ticks can carry both Lyme disease and human granulocytic ehrilichiosis (HGE). IN a study of ticks in the Midwest, it was found that 16% carried Lyme disease, 10% had HGE, and that 10% of the ticks that had either Lyme disease or HGE carried both diseases.

(a) What is the probability P[LH] that a tick carries both Lyme disease (L) and HGE (H)?

My Part:
I don't know how to interpret this problem. Let me show my work thus far.

P[L] = 0.16
P[H] = 0.1

Now this last part, how do I interpret this..."10% of the ticks that had either Lyme disease or HGE carried both diseases."

Like this? given that the ticks had L or HGE, then the ticks that both diseases. So I would write this as:

P[LH | (L U H)] = 0.1

I don't know if this is right though. Any help would be awesome, thanks!

another thought I had was:
P[LH|L] + P[LH|H] = 0.1

This was the first one I did, but I got a probability of something like 0.006 which seems WAY to low.

 

[quasar987]

P[LH | (L U H)] = 0.1 sounds correct.

It is the probability that a deer has L AND H knowing that it has L OR H. It is basically what the problem is saying but it speaks in percentage of a quantity instead of in probability.