To find the predicted number of blue marbles in the bag of 600 marbles, we can use the proportion of blue marbles counted.
Conor found 3 blue marbles out of 10 total marbles. This gives us a proportion of:
\[ \text{Proportion of blue marbles} = \frac{3}{10} = 0.3 \]
Now, we can apply this proportion to the total number of marbles in the bag (600):
\[ \text{Number of blue marbles} = 0.3 \times 600 = 180 \]
Thus, we predict that there will be 180 blue marbles in the bag.