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For two events A and B, if P(A)=0.6P(A) = 0.6, P(B)=0.5P(B) = 0.5 and P(A∪B)=0.8P(A\cup B) = 0.8. Then which of the following statements are TRUE ?

A. P(A∩B)=0.3P(A\cap B) = 0.3.

B. A and B are independent events.

C. P(A′∩B′)=0.2P(A'\cap B') = 0.2.

D. A and B are mutually exclusive events.

Choose the correct answer from the options given below:

Solution

✅ Correct Option: 1

P(A∩B)=0.6+0.5−0.8=0.3P(A\cap B)=0.6+0.5-0.8=0.3, so A is true.

P(A)P(B)=0.30=P(A∩B)P(A)P(B)=0.30=P(A\cap B), so they are independent; B is true.

P(A′∩B′)=1−P(A∪B)=0.2P(A'\cap B')=1-P(A\cup B)=0.2, so C is true.

Since P(A∩B)≠0P(A\cap B)\neq 0, they are not mutually exclusive; D is false.

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