Three fair coins are tossed independently. \(T\) is the event that two or more tosses result in heads. \(S\) is the event that two or more tosses result in tails.
What is the probability of the event \(T \cap S\) ?
Answer
(A)
Explanation
\(T \cap S\) needs at least two heads and at least two tails, which takes at least four tosses. With three coins, two or more heads leave at most one tail, so the two events can never happen together.
\(T\) and \(S\) are mutually exclusive (in fact complementary, since every outcome of three tosses has a majority of heads or a majority of tails), so \(P(T \cap S) = 0\). The value 0.5 is \(P(T)\) alone.
Answer: A