In a sample space S there are 3 events A, B, and C, such that A U B U C =S. A and B are mutually exclusive. P(A)=0.5 and P(B)=0.2.

Prove or disprove that P(C)=0.1.

**Subject Computer Science Discrete Math**

In a sample space S there are 3 events A, B, and C, such that A U B U C =S. A and B are mutually exclusive. P(A)=0.5 and P(B)=0.2.

Prove or disprove that P(C)=0.1.

Prove or disprove that P(C)=0.1.

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Because A and B are mutually exclusive (or disjoint) => P (A U B)=P(A)+P(B)= 0.5 + 0.2 =0.7 and P (A∩ B)=0.

Also, since A U B U C = S => P(A U B U C)=1.

We can write:

...

Also, since A U B U C = S => P(A U B U C)=1.

We can write:

...

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