Assuming a query can refer to logins (logging into Gmail), reads (email open) , deletes, and writes (send),

Here is how I have tried to solve it:

# of queries = # of users per day * #queries per user.

We can divide the users as professional (enterprise) and personal users. Last I read online the daily active user count of gmail was 1B users. I am assuming that 20% of these are professional and 80% are personal accounts.

I will first calculate the professional queries per day and then personal queries per day.

Professional Queries per day:

1. 200M (pro users)

2. Assuming on average, everyday a professional reads 50 emails, writes to 25 of them, and deletes 5 of them. The number of queries that a given professional had done per day = 80.

3. Total professional queries = 200 * 10^6 * 80 --> 16 x 10^9. (part a)

Personal Queries:

We have the remainder 800M users. I am assuming a uniform age distribution for these users. I am also assuming that these users are primarily in the age group 15 - 65. I will further segment these users based on their usage. Also I will assume that Gmail penetration amongst all users is

15-20 (moderate users) = 5/100*800M --> 40M

I am assuming moderate users get 10 email (read), write 5 emails and delete none perday. = 15 query per day

20-50 (power users) = 30/100*800M --> 240M

I am assuming power users get 20 email (read), write 5 emails and delete 5 perday. = 40 query per day

50 - 65 (casual users) = 15/100*800M --> 120M

I am casual users get 5 email (read), write 1 emails and delete 0 perday. = 6 query per day

Thus total query per day for personal users = (40M * 15)+ (240M*40)+(120M*6). -- (part b)

Thus the total number of queries per day = part a + part b.

Any thoughts on this approach?

(edited)