Venn diagrams, two-way tables and set notation

Using set notation (union, intersection, complement, n(A)), Venn diagrams and two-way tables to count outcomes and find probabilities.

Set notation

Counting a union

$$n(A \cup B) = n(A) + n(B) - n(A \cap B)$$

Example 1●●

Of $50$ students, $30$ like maths, $25$ like science and $12$ like both. Find $P(\text{neither})$.

$n(M \cup S) = 30 + 25 - 12 = 43$

Neither $= 50 - 43 = 7$, so $P = \dfrac{7}{50}$.

Example 2●●

$\xi = \{1, 2, \ldots, 12\}$, $A$ = factors of $12$, $B$ = even numbers. Find $n(A \cap B)$.

$A = \{1, 2, 3, 4, 6, 12\}$, $B = \{2, 4, 6, 8, 10, 12\}$

$A \cap B = \{2, 4, 6, 12\}$, so $n(A \cap B) = 4$.

Flashcards

$A cap B$

Intersection: in both

$A cup B$

Union: in either

$n(A')$

$n(\xi) - n(A)$

Practice