Question

In a Press Conference, there are 450 foreign journalists. 275 people can speak German, 250 people can speak English, 200 people can speak Chinese and 260 people can speak Japanese. Find the maximum number of foreigners who cannot speak at least one language.

(a) 401

(b) 129

(c) 324

(d) 415

I had been asked this question in class test.

The above asked question is from Addition Theorem on Probability topic in chapter Discrete Probability of Discrete Mathematics

Answer 1

The correct option is (d) 415

For explanation I would say: The total number of journalists = 350.People who speak German = 275 -> people who do not speak German = 75, people who speak English = 250-> people who do not speak English = 100,people who speak Chinese = 200 -> people who do not speak Chinese = 150, people who speak Japanese = 260 -> people who do not speak Japanese = 90. The total number of people who do not know at least one language will be maximum when the sets of people not knowing a particular language are mutually exclusive. Hence, the maximum number of people who do not know at least one language = 75 + 100 + 150 + 90 = 415.