## The Venn Diagram for Three Independent Events

If three events A, B and C are mutually independent, then

Suppose thatandthen

The Venn diagram starts as

This includes the probabilityso subtract this to obtain the diagram below.

Similarly for A and C and B and c respectively.

Subtractto get 0.036

Subtractto get 0.056,

Finally for A, B and C respectively

0.3-(0.096+0.024+0.036)=0.144

0.4-(0.096+0.024+0.056)=0.224

0.2-(0.036+0.024+0.056)=0.084

finally, the outisde, is 1-(0.144+0.224+0.084+0.096+0.024+0.036)=0.336 to give the completed diagram: