Coaching Centre
Venn diagrams and two-way tables
Organising data in Venn diagrams and two-way tables, using "and", "or", "only" and "neither", and finding probabilities.
Venn diagrams
In a class of $30$, $18$ play soccer, $12$ play tennis and $5$ play both.
Fill in the Venn diagram and find $P(\text{neither})$.
Two-way tables
The same data as a table:
| Tennis | No tennis | Total | |
|---|---|---|---|
| Soccer | $5$ | $13$ | $18$ |
| No soccer | $7$ | $5$ | $12$ |
| Total | $12$ | $18$ | $30$ |
Class of $30$: $18$ soccer, $12$ tennis, $5$ both. Find $P(\text{neither})$.
$5$ neither.
Same class. Find $P(\text{soccer or tennis})$.
$25$ out of $30$.
Same class. Find $P(\text{tennis only})$.
$12 - 5 = 7$.
Same class. How many play soccer only?
$18 - 5$.
Same class. Find $P(\text{soccer and tennis})$.
$5$ out of $30$.
Of $40$ people, $25$ like tea, $20$ like coffee and $13$ like both. How many like neither?
Tea or coffee $= 25 + 20 - 13 = 32$, so $40 - 32 = 8$.
$A \cup B$ means:
The union is everything in at least one set.
Of the $18$ soccer players, what fraction also play tennis?
$5$ out of $18$.
New numbers every time. Keep going until you get five in a row.