A reliable method
- Identify the event and the conditioning group.
- Use the relevant cell or cells in the numerator.
- For a conditional probability use only the conditioning-group total.
- Check that each count comes from the stated table.
Example 1
A club has 12 Grade 7 bus riders and 8 Grade 7 walkers, plus 18 Grade 8 bus riders and 12 Grade 8 walkers. Given that a member is in Grade 7, find the probability of bus travel.
- Restrict attention to Grade 7.
- Its total is 12+8=20; 12 use a bus.
- The conditional probability is 12/20=3/5.
Answer: \(3/5\)
Example 2
Using the same club counts, find the probability that a random member is both Grade 8 and a walker.
- Use the joint cell: 12 Grade 8 walkers.
- The whole club has 12+8+18+12=50 members.
- Joint probability is 12/50=6/25.
Answer: \(6/25\)
Common mistakes
- The whole-table total is not always the correct denominator.
- The probability of A given B need not equal the probability of B given A.
Practice without the answer first
- Using those counts, given bus travel, find the probability that the member is Grade 8.
- A sample has 40 employed adults: 10 cycle and 30 do not. It also has 20 other adults: 8 cycle and 12 do not. Given employment, find the cycling proportion.
- Using the adult sample above, find the proportion of all cyclists who are employed.
Answers and step-by-step explanations
Practice 1
- The conditioning group is all bus riders.
- There are 12+18=30 bus riders, of whom 18 are Grade 8.
- 18/30=3/5.
Answer: \(3/5\)
Practice 2
- Restrict to the 40 employed adults.
- Ten of these cycle.
- 10/40=1/4, not 10/60.
Answer: \(1/4\)
Practice 3
- There are 10+8=18 cyclists.
- Ten cyclists are employed.
- The requested conditional proportion is 10/18=5/9.
Answer: \(5/9\)
These original skill exercises are not official exam questions or a score prediction. Use the coverage notes on your exam hub to choose relevant practice.
