A doctor is called to see a sick child. The doctor knows (prior to the visit) that 90% of the sick children in that neighbourhood are sick with the flu, denoted by `F ,`while 10% are sick with the measles, denoted by `M` A well-known symptom of measles is a rash, denoted by R. The probability having a rash for a child sick with the measles is 0.95. however, occasionally children with the flu also develop a rash, with conditional probability 0.08. upon examination the child, the doctor finds a rash. The what is the probability that the child has the measles? (A) `91/165` (B) `90/163` (C) `82/161` (D) `95/167`

Options

A. `91//165`
B. `90//163`
C. `82//161`
D. `95//167`

Explanation

To solve the problem, we will use Bayes' theorem, which allows us to find the probability of an event given prior knowledge of conditions related to the event.

### Step-by-Step Solution:

1. **Define the Events:**
- Let \( M \) be the event that the child has measles.
- Let \( F \) be the event that the child has the flu.
- Let \( R \) be the event that the child has a rash.
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