Events A and B are such that P(not A or not B) = 0.44. State whether A and B are mutually exclusive events. (Yes/No)

Yes

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Solution

The correct option is B
No

P(not A or not B) =P(A’ $\cup$ B’) = 0.44

P(A’ $\cup$ B’) = P((A $\cap$ B)’) = 0.44 ……………………… (1)

P(A $\cap$ B) = 1 – P((A $\cap$ B)’)

= 1- 0.44

= 0.56 ……………………………… (2)

Two events A and B are mutually exclusive if P(A $\cap$ B) = 0

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Events A and B are such that P(not A or not B) = 0.44. State whether A and B are mutually exclusive events. (Yes/No)

The correct option is B No P(not A or not B) =P(A’∪B’) = 0.44 P(A’∪B’) = P((A∩B)’) = 0.44 ……………………… (1) P(A∩B) = 1 – P((A∩B)’) = 1- 0.44 = 0.56 ……………………………… (2) Two events A and B are mutually exclusive if P(A∩B) = 0