This question was previously asked in

SSC CGL Tier-II ( JSO ) 2016 Official Paper ( Held On : 2 Dec 2016 )

- 1 / 4
- 1 / 2
- 1 / 3
- 2 / 3

Option 4 : 2 / 3

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10 Questions
10 Marks
7 Mins

**Given**

P(A ∩ B) = 1/2,

P(Ac ∩ Bc) = 1/2

2P(A) = P(B) = p

**Formula**

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

**Calculation**

According to the question

⇒ P(A ∪ B) = p/2 + p - 1/2

⇒ P(A ∪ B) = 3p/2 - 1/2

⇒ P(A ∪ B) = 1 - P(Ac ∩ Bc)

⇒ P(Ac ∩ Bc) = 1 - 1/2

⇒ P(Ac ∩ Bc) = 1/2

⇒ 3p/2 - 1/2 = 1/2

⇒ 3p/2 = 1

**∴ The value of p is 2/3**

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