Let the probability of getting the required picture be 0.05 (since there is 1 desired picture out of 20).

1. The probability that Richard does not complete his collection is calculated by not getting the required picture in all 5 attempts:

   \((0.95)^5 = 0.774\)

2. The probability that he has the required picture exactly once is calculated using the binomial probability formula:

   \((0.95)^4 \times (0.05)^1 \times \binom{5}{1} = 0.204\)

3. The probability that he completes his collection with the third picture he looks at is calculated by not getting the picture in the first two attempts and getting it on the third:

   \((0.95)^2 \times (0.05) = 0.0451\)