Conditional Probability SAT — SAT Math Guide
Conditional probability SAT questions test your ability to find the likelihood of an event occurring given that another event has already happened. This concept appears frequently in the Problem Solving and Data Analysis domain, making up about 2-3 questions on the Digital SAT. You'll master this topic quickly once you understand the key formula and practice with realistic examples.
What You Need to Know
Conditional probability measures the chance of event A happening when event B has already occurred
Written as P(A|B), read as "probability of A given B"
Always work with the reduced sample space (the condition limits your options)
Two-way tables and Venn diagrams are common question formats
Independence means P(A|B) = P(A) — the condition doesn't change the probability
📐 KEY FORMULA: P(A|B) = P(A and B) / P(B)
💡 PRO TIP: When using tables, focus only on the row or column that matches your condition.
How to Solve Conditional Probability on the SAT
Example Question 1 — Medium Difficulty
A survey of 200 students asked about their favorite subject. The results are shown in the table below:
| | Math | Science | English | Total |
|----------|------|---------|---------|-------|
| Freshman | 25 | 15 | 10 | 50 |
| Senior | 30 | 45 | 75 | 150 |
| Total | 55 | 60 | 85 | 200 |
What is the probability that a randomly selected senior prefers English?
A) 75/200
B) 75/150
C) 75/85
D) 150/200
Solution:
Step 1: Identify the condition — we're looking at seniors only
Step 2: Find the total number of seniors: 150
Step 3: Find how many seniors prefer English: 75
✅Answer: B — We use only the senior row, so it's 75 seniors who prefer English out of 150 total seniors.
Example Question 2 — Hard Difficulty
At a company, 60% of employees work remotely, and 40% work in the office. Among remote workers, 30% have advanced degrees. Among office workers, 50% have advanced degrees. If an employee is randomly selected and has an advanced degree, what is the probability they work remotely?
A) 0.18
B) 0.30
C) 0.38
D) 0.47
Solution:
Step 1: Calculate employees with advanced degrees who work remotely: 0.60 × 0.30 = 0.18
Step 2: Calculate employees with advanced degrees who work in office: 0.40 × 0.50 = 0.20
Step 3: Total employees with advanced degrees: 0.18 + 0.20 = 0.38
Step 4: Apply conditional probability: P(Remote|Advanced) = 0.18/0.38 ≈ 0.47
✅Answer: D — Among all employees with advanced degrees, 47% work remotely.
Common SAT Math Mistakes to Avoid
❌Mistake: Using the wrong denominator by forgetting to apply the condition
✅Fix: Always identify what group the condition restricts you to, then use only that group's total
❌Mistake: Confusing P(A|B) with P(B|A) — these are different probabilities
✅Fix: Read carefully to identify which event is the condition (comes after "given")
❌Mistake: Adding probabilities instead of using the conditional formula
✅Fix: Remember conditional probability always divides favorable outcomes by the restricted total
❌Mistake: Using the entire sample when a condition is given
✅Fix: Focus only on the row, column, or section that matches your condition
Practice Question — Try It Yourself
A medical test is 95% accurate for people who have a disease and 90% accurate for people who don't have the disease. If 2% of the population has the disease, what is the probability that a person who tests positive actually has the disease?
A) 0.02
B) 0.16
C) 0.95
D) 0.98
Show Answer
Answer: B — Use P(Disease|Positive) = (0.02 × 0.95) / [(0.02 × 0.95) + (0.98 × 0.10)] ≈ 0.16
Key Takeaways for the SAT
Conditional probability always involves a restricted sample space based on given information
The formula P(A|B) = P(A and B) / P(B) works for all SAT math conditional probability problems
Two-way tables are your friend — they organize the information clearly
When you see "given that" or "among those who," you're dealing with conditional probability
Practice identifying which event is the condition and which is the outcome you want
Related SAT Math Topics
Strengthen your SAT math prep with these related topics:
Two way tables →
Probability basics →