JEE Mains · Maths · STD 11 - 14. probability
If \(A\) and \(B\) are two events such that \(P\left( {A \cup B} \right) = P\left( {A \cap B} \right)\), then the incorrect statement amongst the following statements is
- A \(A\) and \(B\) are equally likely
- B \(P\left( {A \cap B'} \right) = 0\)
- C \(P\left( {A' \cap B} \right) = 0\)
- D \(P\left( A \right) + P\left( B \right) = 1\)
Answer & Solution
Correct Answer
(D) \(P\left( A \right) + P\left( B \right) = 1\)
Step-by-step Solution
Detailed explanation
Let \(A\) and \(B\) be two events such that \(\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A} \cap \mathrm{B})\) and \(\mathrm{P}(\mathrm{A} \cup \mathrm{B})=\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})\) option (a) : since…
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