Question

There are a total of 50 distinct books on a shelf such as 20 math books, 16 physics books, and 14 chemistry books. Find is the probability of getting a book that is not a chemistry book or not a physics book.

(a) \(\frac{4}{17}\)

(b) \(\frac{43}{50}\)

(c) \(\frac{12}{31}\)

(d) 1

I got this question by my college professor while I was bunking the class.

Enquiry is from Addition Theorem on Probability in chapter Discrete Probability of Discrete Mathematics

Answer 1

Right answer is (d) 1

Easiest explanation: The probability of not getting chemistry book = 1 – (probability of chemistry book)

= 1 – \(\frac{14}{30} = \frac{16}{30}\) and the probability of not getting chemistry book = 1 – (probability of physics book) = 1 – \(\frac{16}{30} = \frac{14}{30}\). So, the required probability is = \(\frac{16}{30} + \frac{14}{30}\) = 1.