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Question: Answered & Verified by Expert
A coin is tossed three times. Consider the following events:
A: No head appears
B: Exactly one head appears
C: At least two heads appear Which one of the following is correct?
MathematicsSets and RelationsNDANDA 2016 (Phase 2)
Options:
  • A $(\mathrm{A} \cup \mathrm{B}) \cap(\mathrm{A} \cup \mathrm{C})=\mathrm{B} \cup \mathrm{C}$
  • B $\left(\mathrm{A} \cap \mathrm{B}^{\prime}\right) \cup\left(\mathrm{A} \cap \mathrm{C}^{\prime}\right)=\mathrm{B}^{\prime} \cup \mathrm{C}$
  • C $\mathrm{A} \cap\left(\mathrm{B}^{\prime} \cup \mathrm{C}^{\prime}\right)=\mathrm{A} \cup \mathrm{B} \cup \mathrm{C}$
  • D $A \cap\left(B^{\prime} \cup C^{\prime}\right)=B^{\prime} \cap C$
Solution:
2151 Upvotes Verified Answer
The correct answer is: $A \cap\left(B^{\prime} \cup C^{\prime}\right)=B^{\prime} \cap C$
$\quad U=\{(H H H)(H H T)(H T H)(H T T)(T H H)(T H T)(T T H)(T T T)\}$
$A=\{(T T T)\}$
$B=\{(H T T)(T H T)(T T H)\}$
$C=\{(H H H)(H H T)(H T H)(T H H)\}$
By checking the options
(d) $A \cap\left(B^{\prime} \cup C^{\prime}\right)=B^{\prime} \cap C^{\prime}$ is correct.

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