Question 1097130
The total number of balls in the bag = t + 2
Then probability of selecting two orange balls = P(O) = (t/(t+2))*(t/(t+2)) = (t/(t+2))^2
And the probability of selecting two yellow balls = P(Y) = (2/(t+2))^2
So the total probability of selecting two balls of the same color = 
P(O) + P(Y) = t^2/(t+2)^2 + (2/(t+2))^2 = 52/100
Solve for t:
t^2/(t+2)^2 + 4/(t+2)^2 = (t^2+4)/(t+2)^2 = 13/25
This simplifies to 
3t^2 - 13t + 12 = 0
and factors as (3t-4)(t-3) = 0
The solutions are t = 4/3, t = 3
There must be an integer number of balls, so t = 3
Thus there are 3 + 2 = 5 balls in the bag
Check:
P(O) + P(Y) = 3/5*3/5 + 2/5*2/5 = 9/25 + 4/25 = 13/25