Question

A monkey, type words of three letters randomly on a computer. Which is the probability that...

A monkey, type words of three letters randomly on a computer. Which is the
probability that you write a word formed by a consonant followed by two vowels?
The word does not necessarily have to make sense. For simplicity suppose that the keyboard It has 100 keys.

Math   Statistics-And-Probability   
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Answer #1

There are a total of 26 alphabets of which 21 are consonants and 5 are vowels.

The keyboard has a total of 100 keys (which include these 26 alphabets)

Probability = Favorable Outcomes / total Outcomes

We assume that repetition is allowed (as the monkey is pressing keys randomly, the same key could be pressed twice or thrice)

Favorable Outcomes = A consonant in the first place, any of the 5 vowels in the second place and any of the five vowels in the last place. Therefore Total Favorable outcomes = 21 * 5 * 5 = 525

Total Outcomes = Hitting any of the 100 keys each time = 100 * 100 * 100 = 1000000

Therefore the required probability = 525 / 1000000 = 0.000525

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