Some Key Probability Terms

Independent Events If two events A and B are such that B does not in any way affect A then A and B are said to be independent. If B does affect A then the events are said to be dependent.

Independent events examples Tossing a coin or throwing a dice is an independent event since each time the coin is tossed or the dice is thrown we have the same chance of obtaining say a head or a six. Even if we have already tossed a coin 100 times, the next time we toss it we still have an even chance of obtaining a head. So even though I’ve thrown the dice 10 times already, the next time I throw it, I will still have a one in six chance of getting a 6!

Dependent events example With dependent events, what happened before does affect the next event. Imagine you are running a raffle and you have sold 100 tickets and that people are only allowed to buy 1 ticket each. If there are 3 prizes, the chance of wining the 1st prize is 1/100 but the chance of wining the 2nd prize is 1/99 because we only have 99 tickets left to choose from. Similarly the chance of wining the 3rd prize is 1/98 for the same reason. Who’d like to buy a raffle ticket? First prize, a trip to Paris.

Exhaustive An event is said to be exhaustive if we can identify all the possible outcomes.

Exhaustive event example Throwing a dice is exhaustive since we can identify and list all the possible outcomes i.e. we can obtain 1, 2, 3, 4, 5 or 6 spots. Similarly, drawing a card from a deck of cards is exhaustive since we can identify all the possible outcomes. There are 4 aces in this deck of 52 cards. I need an ace to win!

Non-exhaustive event example In ‘real life’ situations, it is often not possible to list all the possible outcomes as ‘objects’ may behave in unpredictable and unknowable ways. For example it is possible to identify all the ways people might respond in an emergency situation? Look out! Horses on the loose. What are they going to do?

Mutually exclusive events Mutually exclusive means that obtaining one result prevents another from happening i.e. we cannot have all the outcomes happening at the same time. The total sum of the probabilities of mutually exclusive events is equal to 1.

Example of mutually exclusive events Tossing a coin is a mutually exclusive event since we cannot get both heads and tails at the same time. This is also true of throwing a dice. When I toss this coin I will get either a head or a tail. I cannot get both at the same time! P(Head) + P(Tail) = 1

Example of events which are not mutually exclusive Here we can have more than one outcome happening at the same time, for example imagine we are listing our outcomes for ‘the weather’. We might list: Sunny Windy Rainy Snowy Stormy and so on (we may not able to list all the possible outcomes!) However, what we actually get is sun and rain at the same time so our outcomes were not mutually exclusive.