Question
A survey conducted at a local high school asked students whether they participate in sports, music programs, or both. The results showed that 60% of the surveyed students participate in sports, 40% participate in music programs, and 20% participate in both sports and music programs.
What is the probability that a student chosen at random from those surveyed participates in either sports or music programs?
Question 7 options:
0.8
0.4
0.6
1
What is the probability that a student chosen at random from those surveyed participates in either sports or music programs?
Question 7 options:
0.8
0.4
0.6
1
Answers
GPT-4o mini
To find the probability that a student participates in either sports or music programs, we can use the principle of inclusion-exclusion.
Let:
- \( P(S) \) = probability of participating in sports = 0.6
- \( P(M) \) = probability of participating in music programs = 0.4
- \( P(S \cap M) \) = probability of participating in both sports and music programs = 0.2
Using the formula for the probability of either event occurring:
\[
P(S \cup M) = P(S) + P(M) - P(S \cap M)
\]
Substituting the known values:
\[
P(S \cup M) = 0.6 + 0.4 - 0.2 = 0.8
\]
So, the probability that a student chosen at random participates in either sports or music programs is:
**0.8**
Therefore, the correct answer is:
**0.8**
Let:
- \( P(S) \) = probability of participating in sports = 0.6
- \( P(M) \) = probability of participating in music programs = 0.4
- \( P(S \cap M) \) = probability of participating in both sports and music programs = 0.2
Using the formula for the probability of either event occurring:
\[
P(S \cup M) = P(S) + P(M) - P(S \cap M)
\]
Substituting the known values:
\[
P(S \cup M) = 0.6 + 0.4 - 0.2 = 0.8
\]
So, the probability that a student chosen at random participates in either sports or music programs is:
**0.8**
Therefore, the correct answer is:
**0.8**