Let's solve this problem together! The set U contains all integers from 1 to 20, inclusive, so it has 20 - 1 + 1 = 20 elements.

The set E2 contains all multiples of 4 from 1 to 20, which are 4, 8, 12, 16, and 20, so it has 5 elements. The probability of picking an integer from U that is in E2 is 5/20 = 1/4.

Therefore, the probability of picking an integer from U that is not in E2 is 1 - 1/4 = 3/4.

OR

The set \(U\) contains integers from 1 to 20 (inclusive), and \(E2\) contains the integers that are multiples of 4 from the set \(U\).

To find the probability that an integer picked at random from \(U\) is not in \(E2\), we need to count the integers that are not multiples of 4 in \(U\), which are the numbers 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18 and 19.

There are 15 such integers. Since there are 20 integers in total in \(U\), the probability of picking an integer that is not in \(E2\) is:

\(P(\text{not in } E2) = \frac{\text{number of integers not in } E2}{\text{total number of integers in } U} = \frac{15}{20} = \frac{3}{4}\)