if events a and b are mutually exclusive are they also collectively exhaustive
Collectively exhaustive events One example of an event that is both collectively exhaustive and mutually exclusive is tossing a coin. The outcome must be either heads or tails, or p (heads or tails) = 1, so the outcomes are collectively exhaustive. When heads occurs, tails can't occur, or p (heads and tails) = 0, so the outcomes are also mutually exclusive.
Spurious relationship In statistics, a spurious relationship or spurious correlation[1][2] is a mathematical relationship in which two or more events or variables are not causally related to each other, yet it may be wrongly inferred that they are, due to either coincidence or the presence of a certain third, unseen factor (referred to as a "common response variable", "confounding factor", or "lurking variable").