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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
A fair coin is tossed three times. Let A be the event of getting exactly two heads and B be the event of getting at most
two tails, then P(AUB) is:
Solution
Total outcomes when a fair coin is tossed 3 times:
\[ n(S) = 2^3 = 8 \]
Event \(A\): exactly 2 heads = {HHT, HTH, THH}
\[ |A| = 3 \]
Event \(B\): at most 2 tails = all outcomes except {TTT}
\[ |B| = 7 \]
Since every outcome of \(A\) (two heads ⇒ one tail) is included in \(B\), we have:
\[ A \subseteq B \;\;\Rightarrow\;\; A \cup B = B \]
Therefore:
\[ P(A \cup B) = P(B) = \frac{|B|}{8} = \frac{7}{8} \]
Final Answer:
\[ \boxed{\tfrac{7}{8}} \]
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