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Difficulty: MediumTwo-Way Tables and Probability

The table below summarizes the results of a survey about extracurricular participation among 11th-grade and 12th-grade students at a high school.

GradeParticipatesDoes not participate
11th Grade45453030
12th Grade55552020

Based on the table, if a student who participates in extracurricular activities is selected at random, what is the probability that the student is in the 11th grade? (Express your answer as a decimal or a fraction.)

Answer: 0.45

Answer

0.45 (or 9/20)
To find the probability that a student is in the 11th grade given that they participate in extracurricular activities, the sample space is restricted to only those students who participate. According to the table, the total number of students who participate is 45+55=10045 + 55 = 100. Out of these 100100 students, 4545 are in the 11th grade. The probability is therefore 45100\frac{45}{100}, which can be written as 920\frac{9}{20} or 0.450.45.

Step-by-Step Solution

1
Determine the size of the restricted sample space by finding the total number of students who participate in extracurricular activities.
100
The probability is conditional on selecting a student who participates in extracurricular activities, so only the 'Participates' column is considered.
2
Identify the number of students within this restricted group who are in the 11th grade.
45
We count the number of students who are both in the 11th grade and participate in extracurricular activities.
3
Calculate the probability by dividing the number of favorable outcomes by the size of the restricted sample space.
45/100 = 9/20 = 0.45
The probability is the ratio of 11th-grade participants to the total participants.

Key Concept

Conditional Probability from a Two-Way Table
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Topics

Two-Way Tables and Probability

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