To predict how many blue marbles are in the bag of 600 marbles, we can use the proportion of blue marbles Conor found in his sample.
In his sample of 10 marbles, he found 3 blue marbles. The proportion of blue marbles is:
\[ \text{Proportion of blue marbles} = \frac{3 \text{ blue marbles}}{10 \text{ total marbles}} = 0.3 \]
Now, we can apply this proportion to the total number of marbles in the bag:
\[ \text{Number of blue marbles in the bag} = 0.3 \times 600 = 180 \]
So, the prediction for the number of blue marbles in the bag is 180 blue marbles.