Problem Solving & Data Analysis

Probability and Two-Way Tables

Compute probabilities from tables and basic counting. Each question below has a complete worked solution.

This collection of 25 SAT math practice questions on probability and two-way tables is sequenced by difficulty so you can warm up on routine problems and progress to the kind of question that separates a competitive math score from an elite one. The first eight problems are calibrated to roughly easy College Board difficulty — the kind that appears in the first third of the math section. The next ten are medium difficulty: the bread-and-butter of the middle of the test. The final seven push into hard territory, where the question writers add an extra step, hide a sign change, or ask for an unrelated expression after you solve.

Work each question on paper before you look at the worked solution. The solution is there to confirm or correct your work, not to lead you. If you cannot start a problem after 30 seconds, mark it and come back; if you cannot finish after 90 seconds, look at the first line of the solution and try again. That structured exposure to the worked solution — not a glance, not a copy — is the most reliable way to convert a missed question into a permanent skill.

#QuestionDifficultyBand
1 A school surveyed students about a proposed schedule change. Of 35 boys and 58 girls who said yes, a… easy 400-500 Open
2 A school surveyed students about a proposed schedule change. 46 boys and 59 girls said yes; 49 boys … easy 400-500 Open
3 A school surveyed students about a proposed schedule change. Of 76 boys and 80 girls who said yes, a… easy 400-500 Open
4 A school surveyed students about a proposed schedule change. 21 boys and 42 girls said yes; 28 boys … easy 400-500 Open
5 A school surveyed students about a proposed schedule change. Of 51 boys and 78 girls who said yes, a… easy 400-500 Open
6 A school surveyed students about a proposed schedule change. 28 boys and 70 girls said yes; 21 boys … easy 400-500 Open
7 A school surveyed students about a proposed schedule change. Of 57 boys and 74 girls who said yes, a… easy 500-600 Open
8 A school surveyed students about a proposed schedule change. 72 boys and 23 girls said yes; 70 boys … easy 500-600 Open
9 A school surveyed students about a proposed schedule change. Of 22 boys and 69 girls who said yes, a… medium 500-600 Open
10 A school surveyed students about a proposed schedule change. 41 boys and 38 girls said yes; 47 boys … medium 500-600 Open
11 A school surveyed students about a proposed schedule change. Of 23 boys and 60 girls who said yes, a… medium 500-600 Open
12 A school surveyed students about a proposed schedule change. 53 boys and 79 girls said yes; 20 boys … medium 500-600 Open
13 A school surveyed students about a proposed schedule change. Of 79 boys and 28 girls who said yes, a… medium 600-700 Open
14 A school surveyed students about a proposed schedule change. 70 boys and 20 girls said yes; 79 boys … medium 600-700 Open
15 A school surveyed students about a proposed schedule change. Of 37 boys and 72 girls who said yes, a… medium 600-700 Open
16 A school surveyed students about a proposed schedule change. 80 boys and 38 girls said yes; 37 boys … medium 600-700 Open
17 A school surveyed students about a proposed schedule change. Of 79 boys and 53 girls who said yes, a… medium 600-700 Open
18 A school surveyed students about a proposed schedule change. 74 boys and 60 girls said yes; 72 boys … medium 600-700 Open
19 A school surveyed students about a proposed schedule change. Of 20 boys and 48 girls who said yes, a… hard 600-700 Open
20 A school surveyed students about a proposed schedule change. 36 boys and 80 girls said yes; 68 boys … hard 700-800 Open
21 A school surveyed students about a proposed schedule change. Of 55 boys and 30 girls who said yes, a… hard 700-800 Open
22 A school surveyed students about a proposed schedule change. 55 boys and 42 girls said yes; 48 boys … hard 700-800 Open
23 A school surveyed students about a proposed schedule change. Of 31 boys and 28 girls who said yes, a… hard 700-800 Open
24 A school surveyed students about a proposed schedule change. 30 boys and 47 girls said yes; 66 boys … hard 700-800 Open
25 A school surveyed students about a proposed schedule change. Of 23 boys and 31 girls who said yes, a… hard 700-800 Open