If B ⊂ A then : 

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NIELIT Scientific Assistant ECE 5 Dec 2021 Official Paper
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  1. P(A ∩ B̅) ≤ P(A) - P(B)
  2. P(A ∩ B̅) ≥ P(A) - P(B)
  3. P(A ∩ B̅) = P(A) - P(B)
  4. P(A ∩ B̅) = P(A) - P(B̅)

Answer (Detailed Solution Below)

Option 3 : P(A ∩ B̅) = P(A) - P(B)
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The correct option is 3

Concept:

If \( B \subset A \), it means all elements of set B are also in set A.

Using set theory, we know that:

\( A = (A \cap B) \cup (A \cap \bar{B}) \)

The sets \( A \cap B \) and \( A \cap \bar{B} \) are disjoint, so:

\( P(A) = P(A \cap B) + P(A \cap \bar{B}) \)

Since \( A \cap B = B \) (as B is a subset of A), we get:

\( P(A) = P(B) + P(A \cap \bar{B}) \Rightarrow P(A \cap \bar{B}) = P(A) - P(B) \)

 

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