Question

There are 70 patients admitted in a hospital in which 29 are diagnosed with typhoid, 32 with malaria, and 14 with both typhoid and malaria. Find the number of patients diagnosed with typhoid or malaria or both.

(a) 39

(b) 17

(c) 47

(d) 53

I have been asked this question in a national level competition.

My question is based upon Discrete Probability topic in chapter Discrete Probability of Discrete Mathematics

Answer 1

Correct choice is (c) 47

To explain I would say: By using the inclusion-exclusion principle: |T ∪ M| = |T| + |M| – |T ∩ M| = (29 + 32) – (14) = 47. Thus 47 patients are diagnosed with either typhoid or malaria.