To determine the probability that a randomly selected student from a group of 150 students in Year 8 plays football, we need to follow a series of steps:
1. Understand the Total Number of Students:
- The total number of students in Year 8 is given as 150.
2. Identify the Number of Students Who Play Football:
- Out of the 150 students, 45 students play football.
3. Define the Formula for Probability:
- Probability of an event happening is calculated using the formula:
[tex]\[
\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}}
\][/tex]
4. Apply the Formula:
- Here, the "favorable outcomes" are the students who play football, and the "possible outcomes" are the total number of students.
- Therefore, the probability (P) that a student picked at random plays football is:
[tex]\[
P(\text{plays football}) = \frac{\text{Number of students who play football}}{\text{Total number of students}}
\][/tex]
[tex]\[
P(\text{plays football}) = \frac{45}{150}
\][/tex]
5. Simplify the Fraction:
- Simplifying the fraction:
[tex]\[
\frac{45}{150} = \frac{3}{10} = 0.3
\][/tex]
Thus, the probability that a randomly picked student from Year 8 plays football is [tex]\(0.3\)[/tex] or [tex]\(30\%\)[/tex].
Therefore:
- The probability is [tex]\(0.3\)[/tex].
- The total number of students is 150.
- The number of students who play football is 45.
