Question

A dictionary contains the following 9 words: two, mice, three, squeaking, the, blind, deaf, birds, rabbits. What is the probability of randomly generating the phrase three blind mice? 1/81 1/729 1/27 1/19,683

Answer 1

The correct answer is B. 1/729

Explanation:

1. Probability of any of the nine words would be randomly cited.

Using the Laplace Rule, we calculate that probability is 1/9

2. Now let's calculate the probability of any two - word phrase in specific order from those nine in the dictionary. We should remember that the probability of occurrence of two or more statistically independent events is equal to the product of their individual probabilities. So,

1/9 * 1/9 = 1/81

3. Using the same Multiplication Rule, we can calculate the probability of a random generation of the phrase "three blind mice", in that specific order. Because there are other phrases that could be generated with those three words, but in different order. The question was specific about the order.

1/9 * 1/9 * 1/9 = 1/729

The probability of randomly generating the phrase "three blind mice" is 1/729 or 0.137%