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Let A be the set of all strings of decimal digits of length 5. For example 00312 and 19483 are two strings in A. You pick a string from A at random. What is the probability that the string has no 4 in it

 Apr 29, 2021
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Since there are no restrictions on the strings, we can think of this problem as drawing 5 random digits in sequence. There is a 9/10 chance each time we draw to NOT get a 4. Every time we draw, we multiply by 9/10 again until we've draw 5 digits. Thus, the answer is (9/10)^5 :)

 Apr 29, 2021

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