Question

If E1 and E2 are two independent events such that P(E1) = 0.35 and P(E1 ∪ E2) = 0.6 then find P(E₂) ?
1. 7/13
2. 5/13
3. 13/17
4. None of these

Answer 1

Correct Answer - Option 2 : 5/13

CONCEPT:

• If A and B are two events then P(A ∪ B) = P(A) + P(B) - P(A ∩ B)
• If A and B are two independent events then P(A ∩ B) = P(A) × P(B)

CALCULATION:

Given: E1 and E2 are two independent events such that P(E1) = 0.35 and P(E1 ∪ E2) = 0.6

Here, we have to find P(E2)

Let P(E2) = x

∵ E1 and E2 are two independent events

As we know that, if A and B are two independent events then P(A ∩ B) = P(A) × P(B)

⇒ P(E1 ∩ E₂) = P(E₁) × P(E₂)

⇒ P(E1 ∩ E2) = 0.35x

As we know that, if A and B are two events then P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

⇒ P(E1 ∪ E2) = P(E1) + P(E2) - P(E1 ∩ E2)

⇒ 0.6 = 0.35 + x - 0.35x

⇒ 0.65x = 0.25

⇒ x = 5/13

⇒ P(E2) = 5/13

Hence, correct option is 2.