A teacher surveys 64 children on how they travelled to school.20 of the students were in Year 7.The teacher surveyed 30% more students in Year 9 than in Year 7.The rest of the students surveyed were in Year 11.75% of the students in Year 7 walked to school.8 more students in Year 9 walked to school than did not walk.Out of students surveyed, more Year 11 students walked to school than Year 9students.One of these students is picked at randomWrite down the probability that the student chosen will walk to school.......................(4)© CORBETTMATHS 2024
Question
A teacher surveys 64 children on how they travelled to school.20 of the students were in Year 7.The teacher surveyed 30% more students in Year 9 than in Year 7.The rest of the students surveyed were in Year 11.75% of the students in Year 7 walked to school.8 more students in Year 9 walked to school than did not walk.Out of students surveyed, more Year 11 students walked to school than Year 9students.One of these students is picked at randomWrite down the probability that the student chosen will walk to school.......................(4)© CORBETTMATHS 2024
Solution
Step 1: Determine the number of students in each year group.
We know that 20 of the students were in Year 7. The teacher surveyed 30% more students in Year 9 than in Year 7. So, the number of Year 9 students is 20 + 30% of 20 = 20 + 6 = 26 students.
The rest of the students surveyed were in Year 11. So, the number of Year 11 students is 64 (total students) - 20 (Year 7 students) - 26 (Year 9 students) = 18 students.
Step 2: Determine the number of students who walked to school in each year group.
We know that 75% of the students in Year 7 walked to school. So, the number of Year 7 students who walked is 75% of 20 = 15 students.
We know that 8 more students in Year 9 walked to school than did not walk. Since there are 26 students in Year 9, we can set up the equation: x + (x + 8) = 26, where x is the number of students who did not walk. Solving for x gives us x = 9. So, the number of Year 9 students who walked is 9 + 8 = 17 students.
We know that more Year 11 students walked to school than Year 9 students. So, the number of Year 11 students who walked is more than 17. Let's assume it's 18 students for the sake of calculation.
Step 3: Calculate the probability that a student chosen at random will walk to school.
The total number of students who walked to school is 15 (Year 7) + 17 (Year 9) + 18 (Year 11) = 50 students.
The total number of students surveyed is 64.
So, the probability that a student chosen at random will walk to school is 50/64 = 0.78125.
Therefore, the probability that the student chosen will walk to school is approximately 0.78 (rounded to two decimal places).
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