Problem-Solving and Data Analysis · Math
Probability
Probability from two-way tables and simple experiments, including conditional probability and complements.
11 questions in the bank · 3 easier · 4 medium · 4 harder · this domain is ≈15% of the section
What to watch for
Conditional probability changes the denominator. 'Given that the student is in group A' restricts you to that row — that restriction is the entire skill.
How the question is worded
These are the actual stems used in the bank — the SAT reuses a small set of wordings, and recognising them saves time on test day.
- The table summarizes survey responses from 98 students. If one of these students is selected at random, what is the probability that the student chose robotics?
- The table summarizes survey responses from 59 students. If a selected student is one of the morning volunteers, what is the probability that this student prefer trails?
- The table summarizes survey responses from 85 students. If one of these students is selected at random, what is the probability that the student picked mural A?
- The table summarizes survey responses from 84 students. If a selected student is one of the bus riders, what is the probability that this student signed up early?
Worked examples
easyThe probability that a randomly selected ticket wins a prize is 3/5. What is t…
The probability that a randomly selected ticket wins a prize is 3/5. What is the probability that a randomly selected ticket does NOT win a prize?
Answer: 2/5
Explanation
An event and its complement have probabilities summing to 1: 1 − 3/5 = 2/5.
mediumThe table summarizes survey responses from 98 students. If one of these studen…
The table summarizes survey responses from 98 students. If one of these students is selected at random, what is the probability that the student chose robotics?
- A. 15/98
- B. 45/98
- C. 24/49
- D. 45/53
Answer: B. 45/98
Explanation
“Chose robotics” is a column: 15 + 30 = 45 students out of all 98. P = 45/98 = 45/98. Probability = (favorable count)/(total count) — the denominator is everyone unless the question restricts the group.
hardThe table summarizes survey responses from 59 students. If a selected student …
The table summarizes survey responses from 59 students. If a selected student is one of the morning volunteers, what is the probability that this student prefer trails?
- A. 5/8
- B. 20/59
- C. 3/8
- D. 20/39
Answer: A. 5/8
Explanation
“Given the student is one of the morning volunteers” restricts the world to that row: 20 + 12 = 32 students. Of those, 20 prefer trails. P = 20/32 = 5/8. Conditional probability changes the denominator — that is the entire skill.