The parents of a sick child called the doctor to ask her to come to see their child. The doctor knows from experience that in a given year 80% of sick children in that neighborhood have a cold (C), while the other 20% are sick with chickenpox (P). Assume for simplicity that (C U P) = sample space i.e., that there no other sickness in that neighborhood.

A clear symptom of chickenpox is a rash (R). Assume that the probability of having a rash if one has chickenpox is 0.9300. However, occasionally children with a cold also develop a rash, and the probability of having a rash if one has a cold is 0.0900.

1)Find P(R|C).

2)Upon examining the child, the doctor finds a rash. What is the probability that the child has chickenpox?

3)Find the probability that a sick child of this neighborhood has a cold and does not have a rash .

4)What is the probability that a sick child of this neighborhood does not have a rash or does not have a cold?