Educerie · SAT · Math
Problem-Solving and Data Analysis · PSDA.5 Probability and conditional probability
What you must be able to do
| You must be able to | What it looks like on the test |
|---|---|
| Find a simple probability | Favourable ÷ total |
| Read a two-way table | Rows, columns and their totals |
| Find a conditional probability | …given that the student is in Year 12 |
| Tell which total the question means | The whole table, a row, or a column |
| Convert between fraction, decimal and percent | All three appear in options |
1The idea in one paragraph
Probability on this test is counting. The numerator is how many outcomes count as a success and the denominator is how many are possible — and every difficult question here is difficult only because the denominator is not the one you first reach for. The words "given that", "of those", and "among the students who" all say the same thing: use a smaller total.
Circle the denominator before you write anything. In a two-way table it is the whole, a row, or a column, and the sentence tells you which.
2Simple probability
P(event) = favourable outcomes ÷ total outcomes. It always sits between 0 and 1, and the probability of an event not happening is 1 minus the probability that it does.
3Two-way tables and the three denominators
| Passed | Failed | Total | |
|---|---|---|---|
| Year 11 | 84 | 16 | 100 |
| Year 12 | 108 | 42 | 150 |
| Total | 192 | 58 | 250 |
Those last two are the same cell over two different totals, and they are different numbers. The test asks both, in adjacent questions, on purpose.
4Recognising a conditional
The signals are: given that, of those, among, if the student is known to be. Each one restricts the population before the event is considered.
Read the sentence in two halves. The half after "given that" or "among" names the denominator; the other half names the numerator.
5Probability from percentages
Chaining two conditions multiplies them, exactly as successive percentage changes do. Adding them is the error this kind of question is built to catch.
6Expected counts
Questions phrased "how many of the 800 would you expect" are asking for a multiplication, not for a new probability.
Where points are lost
- Using the grand total when the question restricted the group.
- Inverting the condition: P(A given B) is not P(B given A).
- Adding chained probabilities instead of multiplying.
- Forgetting to convert a fraction into the percentage the options use.
- Reading the wrong row or column from the table.
- Giving the count when the probability was asked for, or the reverse.
Work it right
- Read the sentence to the end before touching a number.
- Find the phrase that restricts the group — given that, among, of those.
- Write the denominator down first.
- Then find the numerator inside that group.
- Convert to the form the options use.
Try it
Use this table for Q1–Q3.
| Bought a ticket | Did not | Total | |
|---|---|---|---|
| Members | 120 | 30 | 150 |
| Non-members | 90 | 160 | 250 |
| Total | 210 | 190 | 400 |
Q1. What is the probability that a person chosen at random from the whole group bought a ticket?
A) 0.30 B) 0.525 C) 0.57 D) 0.80
Q2. Given that a person is a member, what is the probability that they bought a ticket?
A) 0.30 B) 0.57 C) 0.75 D) 0.80
Q3. Given that a person bought a ticket, what is the probability that they are a member?
A) 0.30 B) 0.4286 C) 0.5714 D) 0.80
Q4. In a survey, 60% of respondents own a bicycle. Of those, 25% use it daily. What percentage of all respondents own a bicycle and use it daily? (Type your answer.)
Q5. A bag holds 5 red, 8 blue and 7 green counters. One is drawn at random. What is the probability that it is not blue?
A) 0.25 B) 0.35 C) 0.40 D) 0.60
In one breath
Probability here is counting, and every hard question is hard only because the denominator is not the obvious one — given that, of those and among all mean the total shrinks to a row or a column. Write the denominator down before the numerator, keep P(A given B) apart from P(B given A) because they share a cell and differ everywhere else, and remember that chaining two percentages multiplies them.
Answers
Q1. B — 0.525. the whole table 210/400 = 0.525. A is the members who did not buy; C and D use row totals.
Q2. D — 0.80. the members row 120/150 = 0.80. B is the whole-group figure; C is 120/160.
Q3. C — 0.5714. the ticket-buyers column
D is Q2's answer, and the pair exists to test whether you noticed the denominator changed.
Q4. 15. multiply the two conditions
Answering 85 subtracts; answering 25 ignores the first condition.
Q5. D — 0.60. one minus the blue probability
C is P(blue) itself.
Educerie · written from the published College Board* Assessment Framework for the Digital SAT Suite *(Math, Problem-Solving and Data Analysis, skill/knowledge testing point "Probability and conditional probability"). All questions and explanations are original Educerie text. Last reviewed 12 September 2026.
Check your understanding
The main ideas of this note. Tick each one you could do now, in an exam, without looking back up. Anything you cannot tick yet is the part to read again.