1.

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»

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

The best I can explain: There is a \(\frac{1}{6}\) CHANCE of choosing the 4^thpath, 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.



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