14.2 Events and Their Algebra

Sample Space ($S$) has 8 outcomes: $\{HHH, HHT, HTH, HTT, THH, THT, TTH, TTT\}$.

1. Define Sets:

   • $A = \{TTT\}$
   • $B = \{HTT, THT, TTH\}$
   • $C = \{HHT, HTH, THH, HHH\}$ (At least 2 $\implies$ 2 or 3)

2. Check Mutually Exclusive:

   • $A \cap B = \phi$
   • $A \cap C = \phi$
   • $B \cap C = \phi$ Yes, they are pairwise disjoint.

3. Check Exhaustive:

   • $A \cup B \cup C = \{TTT, HTT, THT, TTH, HHT, HTH, THH, HHH\} = S$. Yes, their union is the sample space.

Conclusion: The events are both mutually exclusive and exhaustive.