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Consider the following relations for two events E and F: 1. P(E ∩ F) ≥ P(E) + P(F) - 1 2. P(E ∪ F) = P(E) + P(F) + P(E ∩ F) 3. P(E ∪ F) ≤ P(E) + P(F) Which of the above relations is/are correct?

Consider the following relations for two events E and F: 1. P(E ∩ F) ≥ P(E) + P(F) - 1 2. P(E ∪ F) = P(E) + P(F) + P(E ∩ F) 3. P(E ∪ F) ≤ P(E) + P(F) Which of the above relations is/are correct? Correct Answer 3 only

Given:

1. P(E ∩ F) ≥ P(E) + P(F) - 1

2. P(E ∪ F) = P(E) + P(F) + P(E ∩ F)

3. P(E ∪ F) ≤ P(E) + P(F)

Calculation:

Let,

E = {2, 3, 4} and F = {2, 6, 7}

⇒ Total element in P(E) and P(F) = 3.

E ∩ F = {2}

Total element in P(E ∩ F) is 1.

E ∪ F = {2, 3, 4, 6, 7}

⇒ The total element in P(E ∪ F) is 5.

Statement: 1

P(E ∩ F) ≥ P(E) + P(F) - 1

⇒ 1 ≥ 3 + 3 - 1  which is incorrect.

Statement: 2

P(E ∪ F) = P(E) + P(F) + P(E ∩ F)

⇒ 5 = 3 + 3 + 1  which is incorrect.

Statement: 3

P(E ∪ F) ≤ P(E) + P(F)

⇒ 5 ≤ 3 + 3 which is correct.

∴ Only statement 3 is correct.

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