TS EAMCET · Maths · Probability
If \(\mathrm{A}\) and \(\mathrm{B}\) are two events in a random experiment such that \(\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})=2 \mathrm{P}(\mathrm{A} \cap \mathrm{B})\) then
- A \(P(A)+P(B)=1\)
- B \(P(A)=P(B)\)
- C \(P(A)+P(B)>1\)
- D \(P(A)=0, P(B)=1\)
Answer & Solution
Correct Answer
(B) \(P(A)=P(B)\)
Step-by-step Solution
Detailed explanation
\(P(A)+P(B)=2 P(A \cap B)\) \(\therefore \quad P(A)+P(B)-P(A \cap B)=P(A \cap B)\) But we know that \(\begin{aligned} & P(A)+P(B)-P(A \cap B)=P(A \cup B) \\ & \therefore \quad P(A \cup B)=P(A \cap B) \\ & \Rightarrow \quad P(A)=P(B) . \end{aligned}\)
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