SOLUTION: At the start of flu season, Dr. Anna Ahmeed examines 50 patients over two days. Of those 50 patients, 30 have a headache, 24 have a cold, and 12 have neither symptom. Some patien

Question 1198140: At the start of flu season, Dr. Anna Ahmeed examines 50 patients over two days. Of those 50 patients, 30 have a
headache, 24 have a cold, and 12 have neither symptom. Some patients have both symptoms.
a) Draw a Venn diagram
b) Find the probability that a patient selected at random has just a headache. Express the answer in fraction form lowest terms.
Answer by ikleyn(52817) (Show Source): You can put this solution on YOUR website!
.
At the start of flu season, Dr. Anna Ahmeed examines 50 patients over two days. Of those 50 patients, 30 have a
headache, 24 have a cold, and 12 have neither symptom. Some patients have both symptoms.
a) Draw a Venn diagram
b) Find the probability that a patient selected at random has just a headache. Express the answer in fraction form lowest terms.
~~~~~~~~~~~~~~~~~~~~

                        Step by step


Step 1.  Find the probability that a randomly selected patient has a headache or a cold

             P(at least one of both symptoms) = 1 - P(neither symptom) = 1 -  = .



Step 2.  Find the probability that a randomly selected patient has both symptoms.

         Use the formula

             P(at least one symptom) = P(headache) + P(cold) - P(both symptoms).


         It gives

             P(both symptoms) = P(headache) + P(cold) - P(at least one symptom) =  +  -  = .



Step 3.  The probability that a randomly selected patient has just a headache is

             P(just a headache) = P(at least one symptom) - P(both symptoms) =  -  =   = .    ANSWER

Solved.

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