Whichever number of "a 2" you add, you will never get the expected value equal to 10.    ANSWER


It always will be less than 9.

I'll answer the following sensible problem, which is similar in wording to
what you wrote.

Let n = the number of slips of paper that have a 2 on them we will add to the bag.
Then the number of slips of paper in the bag will be 10+n.

P(drawing a slip with a 7) = , 
Expectation of the value being a 7 = 

P(drawing a slip with a 9) = , 
Expectation of the value being a 9 = 
  
P(drawing a slip with a 2) = , 
Expectation of the value being a 2 = 

Total expectation = 

Set the total expectation equal to 5:







Answer:
You would need to add 8 slips of paper with 2 on them to make the
expected value of drawing one slip of paper randomly from the bag 
equal to 5.
 
[Note: you would NEVER expect to draw a slip with 5 on it because there
are none!  What "expectation" means is "what the average value of all 
umpteen slips of paper would be approximately if you could play the exact 
same game umpteen times, and averaged up your values per game over those
umpteen times you played it.]

Edwin