Question

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 :)

Answer 1

`Pr = 0.59049`

Explanation:

See Comment for Complete Question

Given that A has 5 digits. A digit in A can be chosen from 0 to 9 (10 digits).

However, selection without 4 means that we can only select from 0 to 3 and 5 to 9 (altogether, that is 9 digits)

The probability of selecting a number other than 4 in each of the digit is:

`1st \to (9)/(10)`

`2nd \to (9)/(10)`

`3rd \to (9)/(10)`

`4th \to (9)/(10)`

`5th \to (9)/(10)`

So, the required probability is:

`Pr = 1st * 2nd * 3rd * 4th * 5th`

`Pr = (9)/(10) *(9)/(10) *(9)/(10) *(9)/(10) *(9)/(10)`

`Pr = (9^5)/(10^5)`

`Pr = (59049)/(100000)`

`Pr = 0.59049`