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Sam writes down the numbers 1, 2, 3, ..., 99

 

(a) How many digits did Sam write, in total?

(b) Sam chooses one of the digits written down, at random.  What is the probability that Sam chooses a 0?

(c) What is the sum of all the digits that Sam wrote down?

 Feb 19, 2023
 #1
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1-9 is 9 digits

10-99 is 90 numbers with 2 digits each, 180 digits total.

180+9 is 189 digits

There are 189 digits

 

There are 189 digits, 9 of which are 0: 10, 20, 30, 40, 50, 60, 70, 80, 90

9/189 when simplified is 1/21

1/21 probability of choosing a 0

 

 

This is an arithmetic sequence, to find the sum, take the smallest number and add it on to the largest number, then multiply that by the number of numbers there are and divide it by 2. 

So take what I just said and the expression will look like this 

((1+99)99)/2

=(100x99)/2

=9900/2

=4450 is the answer

 

A) 189 digits

B) 1/21 choosing a 0

C)4450 sum of all digits

 Feb 20, 2023

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