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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