Question

If E1 and E2 are two events such that P(E1) = 0.3, P(E1 ∪ E2) = 0.4 and P(E2) = x then find the value of x such that E1 and E2 are two independent events ?
1. 2/7
2. 1/5
3. 1/7
4. 3/5

Answer 1

Correct Answer - Option 3 : 1/7

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) = 0.3, P(E1 ∪ E2) = 0.4 and P(E2) = x

Here, we have to find the value of 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) = 0.3x

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)

⇒ 0.4 = 0.3 + x - 0.3x

⇒ 0.7x = 0.1

⇒ x = 1/7

Hence, correct option is 3.