Question

There are 6 possible routes (1, 2, 3, 4, 5, 6) from Chennai to Kochi and 4 routes (7, 8, 9, 10) from the Kochi to the Trivendrum. If each path is chosen at random, what is the probability that a person can travel from the Chennai to the via the 4^th and 9^th road?

(a) \(\frac{3}{67}\)

(b) \(\frac{5}{9}\)

(c) \(\frac{2}{31}\)

(d) \(\frac{1}{24}\)

This question was addressed to me in an internship interview.

This is a very interesting question from Multiplication Theorem on Probability in division Discrete Probability of Discrete Mathematics

Answer 1

Correct option is (d) \(\frac{1}{24}\)

The best I can explain: There is a \(\frac{1}{6}\) chance of choosing the 4^th  path, and there is a \(\frac{1}{4}\) chance of choosing the 9^th path. The selection of the path to the Kochi is independent of the selection of the path to the Trivendrum. Hence, by the rule of product, there is a \(\frac{1}{6} * \frac{1}{4} = \frac{1}{24}\) chance of choosing the 4^th-9^th path.