Mutually and Non-Mutually Exclusive Events
Learning Intentions
- I can apply the addition rule.
- I can use the addition rule.
Definition of Mutually Exclusive Events
- Mutually exclusive events mean that both outcomes are exclusive to each other, meaning there is no overlap.
- Mutually = both
- Exclusive = excluding, separate
Example of Mutually Exclusive Events
- Let’s take the sample space of rolling a standard six-sided die.
- If outcome A = odd numbers and
- outcome B = even numbers,
- then
(mutually exclusive, see the definition.)
Definition of Non-Mutually Exclusive Events
- Non-mutually exclusive events mean that both outcomes are not exclusive to each other, meaning there is no overlap.
Example of Non-Mutually Exclusive Events
- Let’s take the sample space of a standard deck of 52 cards (which means excluding jokers).
- If outcome A = card of hearts and
- outcome B = ace card,
= { ace of hearts }
The Addition Rule
The Addition Rule
- This works by adding the probability of the two outcomes (which overlap) and subtracting the overlap.
is ignored in a mutually exclusive scenario.
Standard Application of The Addition Rule (1)
- A card is selected from a standard deck of 52 playing cards (no jokers). Find
.
- A = card of diamonds
- B = jack card
, , - Apply the addition rule to find
.
Standard Application of The Addition Rule (2)
- Two events, A and B, are such that
- Find (a)
and (b) . - (a)
= 0.35
- (b)
(anything not A and not B, complement!)