KCET · Maths · Application of Derivatives
\( A \) and \( B \) are two events such that \( P(A) \neq 0, P(B / A) \) if ,
(i) \( A \) is a subset of \( B \)
(ii) \( A \cap B=\Phi \) are respectively
- A \( 0 \) and \( 1 \)
- B \( 1,0 \)
- C \( 1,1 \)
- D \( 0,0 \)
Answer & Solution
Correct Answer
(B) \( 1,0 \)
Step-by-step Solution
Detailed explanation
Given that \(P(A) \neq 0\)
We know that
\(P(B \mid A)=\frac{P(A \cap B)}{P(A)}\)
So, \(P(B \mid A)=0\)
Since \(P(A) \neq 0\) then \(P(A)=1\)
Now, \(P(A \cap B)=0\)
Since \(A \cap B=\phi\)
So, \(P(B)=0\)
We know that
\(P(B \mid A)=\frac{P(A \cap B)}{P(A)}\)
So, \(P(B \mid A)=0\)
Since \(P(A) \neq 0\) then \(P(A)=1\)
Now, \(P(A \cap B)=0\)
Since \(A \cap B=\phi\)
So, \(P(B)=0\)
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