Probability: Explaining Events

I wrote this explanation for a student in Stats class. Might be useful for students at undergraduate level probability/statistics classes.

(a) Mutually Exclusive Events: Two events or instances are mutually exclusive if they can not occur together. Eg; If you toss a coin Head and Tails are mutually exclusive events. If you roll a die getting a 1 or a 2 are mutually exclusive since you can not get both of them in a single roll. So, in terms of math: probability (Heads or Tails) = prob(Head) + prob(Tails) = 1/2 + 1/2 = 1. Note that there is no prob (Head and Tails) term as prob(Head and Tails) = 0, as they are mutually exclusive. Similarly, prob(1 or 2) = prob(1) + prob (2) = 1/6 + 1/ 6 = 1/3

(b) Collectively Exhaustive Events: are the only possible events! Eg; When you roll a die once collectively exhaustive will be 1,2,3,4,5,6 events. if you toss a coin Heads and Tails are the collectively exhaustive events. so, in terms of math sum of probabilities of collectively exhaustive events is always 1. i.e. prob (head or tails) = 1. prob(1,2,3,4,5,6) = 1.