A monkey randomly hits a keyboard with 26 letters, one per second. (a) How long, in...

A monkey randomly hits a keyboard with 26 letters, one per second.

(a) How long, in average, will it take for the monkey to type the letter Z for the first time?

I believe that each letter is random and independent, meaning that the probability of the monkey typing any letter is (1/26). Therefore, the expected value is equal to the sum from 1 to 26 times (1/26), yielding 13.5 seconds. I am unsure how to move forward with parts (b) and (c).

(b) How long, in average, will it take for the monkey to type the letter Z for the second time?

(c) How long, in average, will it take until the monkey types two Z’s in a row? (Hint: condition on the event that the Monkey types Z on the first second).

Expert Solution

orchestra answered 2 years ago

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