Digital SAT · Math · Problem-Solving and Data Analysis. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A probability is a fraction: the number of outcomes you want over the number of outcomes that are possible. It is always between 0 and 1.
Many SAT questions use a two-way table. The hard part is choosing the right total for the bottom of the fraction. If the question says given that, or picks from one group only ("a student in Grade 10 is selected"), the total is that group's row or column, not the whole table. This is a conditional probability.
For two events in a row, multiply the probabilities. If the first item is not put back, both the number you want and the total go down before the second pick.
Dividing by the grand total when the question limits the choice to one row or column. Read who is being selected from, and use that group's total as the denominator.
Answer: 7/12 (not 42/120, because the choice is only from the 72 students who play a sport)
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