To find the probability that a number selected at random from 41 to 56 is a multiple of 9, we need to count the number of multiples of 9 within that range and then divide it by the total number of possible selections.

The multiples of 9 within the range 41 to 56 are: 45 and 54.

Total possible selections = 56 - 41 + 1 = 16 (since we have to include both endpoints)

Number of multiples of 9 = 2

Now, the probability of selecting a multiple of 9 is given by:

\( \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{2}{16} = \frac{1}{8} \)