Coaching Centre
Mutually exclusive events and the addition rule
Mutually exclusive and non-mutually exclusive events, the addition rule P(A ∪ B) = P(A) + P(B) − P(A ∩ B), and complements.
Mutually exclusive
Events are mutually exclusive if they cannot happen together: $P(A \cap B) = 0$. Rolling a $2$ and rolling a $5$ on one die are mutually exclusive; rolling an even number and a number greater than $4$ are not (both happen with a $6$).
A card is drawn from a standard deck. Find $P(\text{king or heart})$.
Card from a standard deck: $P(\text{king or heart})$?
$\tfrac{16}{52}$.
Die: $P(\text{even or greater than } 4)$?
$\{2, 4, 5, 6\}$.
$P(A) = 0.5$, $P(B) = 0.4$, $P(A \cap B) = 0.2$. Find $P(A \cup B)$.
$0.5 + 0.4 - 0.2$.
$A$ and $B$ are mutually exclusive, $P(A) = 0.3$, $P(B) = 0.4$. Find $P(A \cup B)$.
No overlap.
Are "rolling a $2$" and "rolling a $5$" mutually exclusive?
One roll can't be both.
Are "drawing a red card" and "drawing a queen" mutually exclusive?
The red queens are both.
$P(A \cup B) = 0.8$, $P(A) = 0.6$, $P(B) = 0.35$. Find $P(A \cap B)$.
$0.6 + 0.35 - 0.8$.
Using the previous question, find $P(A \cup B)'$.
$1 - 0.8$.
New numbers every time. Keep going until you get five in a row.