AI HL · 13.1
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Probability from two-way tables
13.1.4
The table shows how 80 students in Year 10 and Year 11 travel to school. A student is chosen at random. Find the probability that the student comes by bus.
Have a go first. Then open the working one line at a time.
Bus row: 14 + 22 = 36. Walk: 9 + 11 = 20. Car: 7 + 17 = 24.
Total every row and every column before you read a probability.
36 + 20 + 24 = 80
The rows and the columns give the same grand total. Use it as a check.
\(P(\text{bus})=\frac{36}{80}=\frac{9}{20}=0.45\)
The row total is the number of students in the event. The grand total is every student.
Use the table in the last example. A student who walks to school is chosen at random. Find the probability that this student is in Year 11.
Have a go first. Then open the working one line at a time.
The student walks: only the Walk row is left. 9 + 11 = 20
The words after 'given' or 'who' tell you which row or column to keep.
Year 11 walkers: 11
Look along the same row for the property you want.
\(P(\text{Year 11}\mid\text{walks})=\frac{11}{20}=0.55\)
The denominator is 20, not 80.
A swimming pool records its 80 visitors by session and age. Find the probability that a visitor chosen at random who did not swim in the morning session is a child.
Have a go first. Then open the working one line at a time.
Morning 30, Afternoon 20, Evening 30. Adult 40, Child 40. Total 80.
Add the rows and the columns.
Not morning: Afternoon + Evening = 20 + 30 = 50
Two rows are left. Their totals add.
Children: 5 + 25 = 30
Add the Child cells of the two rows.
\(P(\text{child}\mid\text{not morning})=\frac{30}{50}=\frac{3}{5}=0.6\)
Fifty visitors are left, so the denominator is 50.