Given the following information about events B and C: P(B)=70% P(B AND C)=0 P(C)=45% Are B and C mutually exclusive, independent, both, or neither?

 Given the following information about events B and C:

P(B)=70%
P(B AND C)=0
P(C)=45%
Are B and C mutually exclusive, independent, both, or neither?

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B and C are both mutually exclusive and independent because P(B AND C)=0
B and C are independent because P(B AND C)=0
B and C are mutually exclusive because P(B AND C)=0.

B and C are neither mutually exclusive nor independent.

Answer Explanation
Correct answer:
B and C are mutually exclusive because P(B AND C)=0.

Since P(B AND C)=0, we can conclude that B and C are mutually exclusive. P(B AND C)≠P(B)⋅P(C), so we cannot conclude that the events are independent.