Three Fair Coins Are Tossed and Either Heads or Tails $$\text { Is } P ( A \cup B ) \text { equal to the sum of } P ( A ) \text { and } P ( B ) \text { ? Explain. }$$

Essay

Three fair coins are tossed and either heads or tails is observed for each coin. Events A and
B are defined as follows.
A: {Three heads are observed}.
B: {Exactly two heads are observed}. $$\text { Is } P ( A \cup B ) \text { equal to the sum of } P ( A ) \text { and } P ( B ) \text { ? Explain. }$$