Alpheus has a bag of 10 marbles, Belinda has a bag of 100 marbles and Tom has a bag of 1,000 marbles. There is one red marble in each of these bags. Without looking into the bag, you pick a marble out of one of the bags. Whose bag would give you the greatest chance of picking the red marble?

Alphons's bag has 1 red marble out of 10 total marbles.

$$P(\text{Alphons}) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = \frac{1}{10}$$

Belinda's bag has 1 red marble out of 100 total marbles.

$$P(\text{Belinda}) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = \frac{1}{100}$$

Tom's bag has 1 red marble out of 1000 total marbles.

$$P(\text{Tom}) = \frac{\text{Number of red marbles}}{\text{Total number of marbles}} = \frac{1}{1000}$$

To compare, we can convert the fractions to decimals:

$$P(\text{Alphons}) = \frac{1}{10} = 0.1$$ $$P(\text{Belinda}) = \frac{1}{100} = 0.01$$ $$P(\text{Tom}) = \frac{1}{1000} = 0.001$$

Comparing the decimal values, 0.1 is the largest. Therefore, Alphons's bag gives the greatest chance of picking the red marble.

The correct option is:
$\text{Alphons's bag}$