# GATE | Sudo GATE 2020 Mock I (27 December 2019) | Question 29

A and B are two independent events and given P(B) = 0.4 ; P(A ⋃ B’) = 0.8. Which one of the following is value of P(A ⋂ B)? (B’ is complement of B).**(A)** 0.5**(B)** 0.4**(C)** 0.3**(D)** 0.2**Answer:** **(D)****Explanation:** According to given data,

→ P(A ⋃ B’) = 0.8 → P(A) + P(B’) - P(A)(B’)= 0.8 → P(A) + 1 - P(B) - P(A)(1 - P(B)) = 0.8 → P(A) + 1 - P(B) - P(A) + P(A)P(B) = 0.8 → P(B) - P(A)P(B) = 0.2 → P(B) - P(A ⋂ B) = 0.2

Since, A and B are independent sets so, P(A ⋂ B)=P(A)P(B)

Now,

P(A ⋂ B) = P(B) - 0.2 = 0.4 - 0.2 = 0.2

So, option (D) is correct.

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