Question

1. using the venn diagram shown, find:

4a ( p(a \text{ but not } b) )
probability =

Explanation:

Step1: Find total number of elements

First, we calculate the total number of elements in the universal set. The elements are in set A only (6), set B only (12), the intersection of A and B (5), and outside both sets (8). So total \( N = 6 + 5 + 12 + 8 = 31 \).

Step2: Find number of elements in A but not B

The number of elements in A but not B is the number of elements only in set A, which is 6.

Step3: Calculate the probability

The probability \( P(A \text{ but not } B) \) is the number of elements in A but not B divided by the total number of elements. So \( P(A \text{ but not } B) = \frac{6}{31} \).

Answer:

\(\frac{6}{31}\)