ACT Preparation / Unit 15 ACT 1427 worked example, 60 to 90 seconds
Conditional Probability From a Table
The idea
A conditional probability is read from a two-way table in three steps. First, find the given condition, the group the question limits you to, which follows a word such as given, if or among. Second, use that row or column total as the denominator. Third, find the count in that row or column that also meets the other condition, and divide.
In practice
Worked example: an invented survey of 200 students records grade and lunch choice. Of 90 juniors, 54 bring lunch; of 110 seniors, 44 bring lunch, so 98 bring lunch in all. P(brings lunch given junior) = 54/90 = 0.6. P(junior given brings lunch) = 54/98, about 0.55. P(junior and brings lunch) = 54/200 = 0.27.
Where people slip
The three questions share a numerator and differ only in the denominator. Choose the denominator from the given condition, or the grand total when there is none.
Your place on the trail
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Unlocks
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