Math  /  Data & Statistics

QuestionYou can sketch yo Fifty students are participating in the school musical. Of those students 12 are on the debate team and 23 are seniors. There are twenty students who are not on the debate team and are not seniors.
If a student is selected at random, what is the probability the student is a senior or on the debate team?

Studdy Solution

STEP 1

1. Total number of students participating in the musical is 50.
2. There are 12 students on the debate team.
3. There are 23 seniors.
4. There are 20 students who are neither on the debate team nor seniors.
5. We need to find the probability that a randomly selected student is either a senior or on the debate team.

STEP 2

1. Use the principle of inclusion-exclusion to find the number of students who are either seniors or on the debate team.
2. Calculate the probability using the total number of students.

STEP 3

Let D D be the set of students on the debate team and S S be the set of seniors.
Given: D=12 |D| = 12 S=23 |S| = 23 DS=20 |D' \cap S'| = 20
Where D D' is the complement of D D and S S' is the complement of S S .

STEP 4

Calculate the number of students who are either seniors or on the debate team using the principle of inclusion-exclusion:
DS=D+SDS|D \cup S| = |D| + |S| - |D \cap S|
First, find DS |D \cap S| :
Since DS=20 |D' \cap S'| = 20 , the number of students who are either seniors or on the debate team is:
DS=5020=30|D \cup S| = 50 - 20 = 30

STEP 5

Calculate the probability that a randomly selected student is either a senior or on the debate team:
P(DS)=DSTotal number of students=3050=0.6P(D \cup S) = \frac{|D \cup S|}{\text{Total number of students}} = \frac{30}{50} = 0.6
The probability that a randomly selected student is either a senior or on the debate team is:
0.6 \boxed{0.6}

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