Probability

For one fair die roll, decide whether each pair is:

• mutually exclusive;

• exhaustive.

Give a reason for each decision.

1. \(A=\{\text{even}\hspace{0.15em}\}\), \(B=\{\text{odd}\hspace{0.15em}\}\).

2. \(C=\{\text{at most}\hspace{0.5em}4\}\), \(D=\{\text{at least}\hspace{0.5em}3\}\).

3. \(E=\{1\}\), \(F=\{6\}\).