On average, 30 minutes TV-shows have 22 minutes of actual pr…

On average, 30 minutes TV-shows have 22 minutes of actual program. Let’s assume the probability distribution for number of minutes of actual program is uniformly distributed from a low of 18 minutes to high of 26 minutes.   What is the probability the show will have between 21 minutes and 25 minutes of programming?

A doctor is called to see a sick child. The doctor has prior…

A doctor is called to see a sick child. The doctor has prior information that 90% of sick children in that neighborhood have the flu, while the other 10% are sick with measles.   A well-known symptom of measles is a rash.  Assume that the probability of having a rash if one has measles is 95%. However, occasionally children with flu also develop rash, and the probability of having a rash if one has flu is 8%.   Upon examining the child, the doctor finds a rash. What is the probability that the child has measles?