What this lesson covers
- "If / given / among" names a group: that group's total is your denominator
- The numerator is the cell inside that row or column
- P(A given B) is NOT P(B given A)
Chapters
- 0:00Four words that change the answer
- 0:26Read the table
- 0:56"Given" restricts the denominator
- 1:38Flip the given, flip the answer
- 2:11Your turn
- 2:47Three traps
- 3:19Recap
Lesson transcript
The narration of the video, word for word, under its chapter headings.
0:00Four words that change the answer
Welcome to SAT Climb. The digital SAT loves one particular kind of data question. A two-way table, and a question that starts with if, or given. Those little words quietly delete part of the table, and if you don't notice, you'll get a clean-looking answer that's completely wrong.
0:26Read the table
Here's our table. A school surveys one hundred students. Grade ten. Eighteen play a sport, twenty-two don't. That row totals forty. Grade eleven. Twenty-seven play, thirty-three don't. Sixty in that row. Down the columns, forty-five athletes, fifty-five non-athletes, one hundred total. Every number sits at the crossing of two facts, a grade and a sport status. That crossing is what the SAT asks about.
0:56"Given" restricts the denominator
The question. If a surveyed student is in grade eleven, what's the probability they play a sport? The word if restricts you. Given grade eleven means the grade ten row is gone. Those forty students no longer exist for this question. Your whole world is the sixty students in the grade eleven row. So the denominator is sixty, not one hundred. The numerator is the sport cell inside that row, twenty-seven. Twenty-seven out of sixty. That's nine twentieths, forty-five percent. If you wrote twenty-seven over one hundred, you used students the question already threw away.
1:38Flip the given, flip the answer
Now watch this. Flip the question. If a student plays a sport, what's the probability they're in grade eleven? Same table, same twenty-seven students on top. But the given changed. Now you live in the sport column, forty-five students. Twenty-seven out of forty-five. Three fifths. Sixty percent. Same cell in the numerator, completely different answer, forty-five versus sixty percent. The rule. Whatever follows given, or if, or among, that group is your denominator.
2:11Your turn
Your turn. If a surveyed student is in grade ten, what's the probability they do not play a sport? Pause if you want to work it. The given is grade ten, so the denominator is that row's total, forty. The no-sport cell in that row is twenty-two. Twenty-two out of forty. Eleven twentieths. Fifty-five percent. If you got fifty-five percent, you restricted the denominator like a pro.
2:47Three traps
Three traps. One, defaulting to one hundred. The moment a question says if or given, the grand total is dead. Two, flipping the condition. Probability of sport given grade eleven is not probability of grade eleven given sport. We just watched forty-five percent become sixty. Three, mixing rows and columns. If the condition names a column group, divide by the column total. The condition always names the group you divide by.
3:19Recap
Two-way tables, solved. Find the given, restrict to that row or column, and divide by its total. The numerator is just the cell inside. Start practicing free at satclimb.com. Your SAT is closer than you think.
Read the written version: the Probability & conditional probability strategy guide, then try 25 hard Probability & conditional probability questions with full explanations. Both are free, no account needed.