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Probability Using Two-Way Table P(Ac or B)
Published on September 2, 2026
Statistics
Learn how to find the probability of the union of two events, P(Ac or B), using a two-way frequency table of student survey data. Follow step-by-step calculations with the addition rule of probability to arrive at the correct answer of 0.82.
Question
Answer
- Identify the given information from the table and the problem description:
- Total students surveyed:
- Event
: Student takes statistics. - Event
: Student is a senior. -
: Student does not take statistics (which, in this context, means the student takes calculus).
- Extract the relevant counts from the table:
- Number of seniors who take calculus:
- Number of juniors who take calculus:
- Number of seniors who take statistics:
- Number of juniors who take statistics:
- Calculate the components for the probability
using the Addition Rule:
- Total students who do not take statistics (
): . So, . - Total seniors (
): . So, . - Seniors who do not take statistics (
): . So, .
- Compute the final probability:
Alternatively, sum the counts of the favorable outcomes:
- Students who are seniors (
): - Students who are not seniors but do not take statistics (
): - Total favorable:
-
0.82