Problem Analysis:
To solve this problem, we need to find the probability that the number of consonants on the right of every vowel is at least one more than the number of vowels on the right of it. We are given five letters to choose from: A, B, E, P, and Q. We need to form a five-letter word without repetition. Let's break down the problem into smaller steps to find the solution.

Step 1: Counting the total number of possible arrangements:
Since we are forming a five-letter word without repetition, the total number of possible arrangements can be calculated using the permutation formula:
Total arrangements = 5P5 = 5! = 120

Step 2: Counting the favorable arrangements:
To count the favorable arrangements, we need to determine the possible positions of vowels and consonants in the word. Let's consider the following cases:

Case 1: Vowel at the first position:
If a vowel is placed at the first position, there are two remaining vowels and two remaining consonants to be placed in the last four positions. The possible arrangements can be calculated as follows:
- First position: 1 option (either A or E)
- Second position: 4 options (A, B, E, P)
- Third position: 3 options (remaining vowel)
- Fourth position: 2 options (remaining consonant)
- Fifth position: 1 option (remaining consonant)

Number of arrangements in this case = 1 * 4 * 3 * 2 * 1 = 24

Case 2: Consonant at the first position:
If a consonant is placed at the first position, there are three remaining vowels and one remaining consonant to be placed in the last four positions. The possible arrangements can be calculated as follows:
- First position: 3 options (B, P, Q)
- Second position: 4 options (remaining letters)
- Third position: 3 options (remaining vowel)
- Fourth position: 2 options (remaining vowel)
- Fifth position: 1 option (remaining consonant)

Number of arrangements in this case = 3 * 4 * 3 * 2 * 1 = 72

Total favorable arrangements:
The total number of favorable arrangements is the sum of arrangements from Case 1 and Case 2:
Total favorable arrangements = 24 + 72 = 96

Step 3: Calculating the probability:
To find the probability, we divide the total favorable arrangements by the total number of possible arrangements:
Probability = (Total favorable arrangements) / (Total arrangements) = 96 / 120 = 4 / 5 = 0.8

Conclusion:
The probability that the number of consonants on the right of every vowel is at least one more than the number of vowels on the right of it is 0.8 or 80%.