Are all non mutually exclusive sets Independent?

GRE Quant Problem Solving
1

Hi P(a) = 0.4 and P(b) = 0.7

This is not mutually exclusive. Are these independent?

In general, Any time I conclude events to be not mutually exclusive, can I also say they are independent.

2

Yes these are not mutually exclusive, but that doesn’t mean that they are independent
You could consider them independent if:

  • The events defined are unrelated to each other for eg. a: Raining, b:eating pasta
  • The question simply states that a and b are independent
  • If P(a \cap b) = P(a)*P(b) = 0.28
1 Like
3

Thank You Vidishas that helps clear a fundamental doubt!