Answer :
Let's go through the solution step-by-step:
In the class, there are 30 students. We have the following information:
- 12 students like soccer.
- 15 students like basketball.
- 5 students like both soccer and basketball.
We are asked to find the probability that a randomly chosen student likes either soccer or basketball.
To solve this, we can use the principle of Inclusion-Exclusion. The formula for the probability that a student likes either soccer or basketball is:
[tex]\[
P(\text{Soccer or Basketball}) = P(\text{Soccer}) + P(\text{Basketball}) - P(\text{Both})
\][/tex]
1. First, calculate the number of students who like either soccer or basketball:
- Add the number of students who like soccer and basketball, then subtract the number of students who like both to avoid double-counting them.
[tex]\[
\text{Students who like either} = 12 + 15 - 5 = 22
\][/tex]
2. Next, calculate the probability by dividing the number of students who like either sport by the total number of students:
[tex]\[
\text{Probability} = \frac{22}{30} = 0.7333\ldots
\][/tex]
The correct probability is approximately 0.73, which corresponds to option B in the question.
In the class, there are 30 students. We have the following information:
- 12 students like soccer.
- 15 students like basketball.
- 5 students like both soccer and basketball.
We are asked to find the probability that a randomly chosen student likes either soccer or basketball.
To solve this, we can use the principle of Inclusion-Exclusion. The formula for the probability that a student likes either soccer or basketball is:
[tex]\[
P(\text{Soccer or Basketball}) = P(\text{Soccer}) + P(\text{Basketball}) - P(\text{Both})
\][/tex]
1. First, calculate the number of students who like either soccer or basketball:
- Add the number of students who like soccer and basketball, then subtract the number of students who like both to avoid double-counting them.
[tex]\[
\text{Students who like either} = 12 + 15 - 5 = 22
\][/tex]
2. Next, calculate the probability by dividing the number of students who like either sport by the total number of students:
[tex]\[
\text{Probability} = \frac{22}{30} = 0.7333\ldots
\][/tex]
The correct probability is approximately 0.73, which corresponds to option B in the question.
