Question

1. In a small city it turns out that 90% of sick children have the flu, while the other 10% are sick with measles. Let F stand for an event of a child being sick with flu and M stand for an event of a child being sick with measles. A well-known symptom of measles is a rash (we will denote this event by R). Assume that the probability of having a rash if one has measles is 0.95 However, occasionally children with flu also develop rash, and the probability of having a rash if one has flu is 0.08. (You may assume that only two illnesses are possible, either the flu or measles.) (i) What is the probability that a sick child has a rash? (ii) A doctor visits a sick child and finds that the child has a rash. What is the probability that the child has measles?

          1. In a small city it turns out that 90% of sick children have the flu, while the
other 10% are sick with measles. Let F stand for an event of a child being
sick with flu and M stand for an event of a child being sick with measles.
A well-known symptom of measles is a rash (we will denote this event by
R). Assume that the probability of having a rash if one has measles is 0.95
However, occasionally children with flu also develop rash, and the probability
of having a rash if one has flu is 0.08. (You may assume that only two illnesses
are possible, either the flu or measles.)
(i) What is the probability that a sick child has a rash?
(ii) A doctor visits a sick child and finds that the child has a rash. What is
the probability that the child has measles?

1. In a small city it turns out that 90% of sick children have the flu, while the
other 10% are sick with measles. Let F stand for an event of a child being
sick with flu and M stand for an event of a child being sick with measles.
A well-known symptom of measles is a rash (we will denote this event by
R). Assume that the probability of having a rash if one has measles is 0.95
However, occasionally children with flu also develop rash, and the probability
of having a rash if one has flu is 0.08. (You may assume that only two illnesses
are possible, either the flu or measles.)
(i) What is the probability that a sick child has a rash?
(ii) A doctor visits a sick child and finds that the child has a rash. What is
the probability that the child has measles?

Added by Brenda C.

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