Question

If a fair 15-sided dice is rolled, then is the probability that the roll is an odd number or prime number or both?

(a) \(\frac{3}{20}\)

(b) \(\frac{4}{19}\)

(c) \(\frac{9}{20}\)

(d) \(\frac{17}{20}\)

I have been asked this question by my school teacher while I was bunking the class.

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

Answer 1

The correct choice is (c) \(\frac{9}{20}\)

Easy explanation: There are 7 even numbers on the 20-sided dice: 1, 3, 5, 7, 9, 13, 15. There are 6 prime numbers on the 20-sided dice: 2, 3, 5, 7, 11, 13. There are 4 numbers that are both odd and prime: 3, 5, 7, 13. By the rule of sum, the probability that an odd or prime number is rolled is \((\frac{7}{20}) + (\frac{6}{20}) – (\frac{4}{20}) = \frac{9}{20}\).