Question

Which option correctly identifies mutually exclusive events for \(S = \{1, 2, 3, 4, 5, 6\}\)?

Options

• \(A = \{1, 2\}\), \(B = \{5, 6\}\), and \(A \cap B = \phi\)

• \(A = \{1, 2\}\), \(B = \{2, 3\}\), and \(A \cap B = \{2\}\)

• \(A = \{1, 2, 3\}\), \(B = \{3, 4\}\), and \(A \cap B = \{3\}\)

• \(A = \{1, 2, 3\}\), \(B = \{1, 2\}\), and \(A \cap B = \{1, 2\}\)

Answer 1

Mutually exclusive events cannot happen together. The sets \(\{1, 2\}\) and \(\{5, 6\}\) have no common element, so their intersection is empty.