Keyboard and monkey
Probability
Level
2
A monkey is placed in front of a keyboard with only the 26 letters of the alphabet on it.
The monkey strikes a key at random 10,000,000,000 times.
What is the expected number of occurrences of the string of letters COVFEFE?
Between 6 and 9
Between 3 and 6
Less than 3
More than 9
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1 solution
To generate a 7-letter string at random, the monkey has to hit the "correct" key 7 times in a row. This has a probability of 2 6 − 7 , or approximately 1 chance in 8,000,000,000.
So the expected number of occurrences of the string COVFEFE with 10,000,000,000 keys struck is about 1.25.