Final answer:
The probability that Dixie will not choose a penny is 11/15.
Step-by-step explanation:
To find the probability that Dixie will not choose a penny, we need to calculate the ratio of the number of non-penny coins to the total number of coins in the bag. Dixie has 10 dimes, 1 nickel, and 4 pennies, so there are 10 + 1 = 11 non-penny coins. The total number of coins in the bag is 10 + 1 + 4 = 15. Therefore, the probability that Dixie will not choose a penny is 11/15 or 11/15.