The table shows the shoe size of 23 students.
A student is picked at random.
| Shoe Size | Frequency |
| --------- | --------- |
| 5 | 2 |
| 6 | 11 |
| 7 | 5 |
| 8 | 4 |
| 9 | 1 |
(a) Work out the probability that the student has a shoe size of 8.
(b) Work out the probability that the student has a shoe size of 7 or smaller.
Answer (1)
Calculate the probability of a student having shoe size 8: 23 4 .
Calculate the probability of a student having shoe size 7 or smaller: 23 2 + 11 + 5 = 23 18 .
The probability that a student has a shoe size of 8 is: 23 4 .
The probability that a student has a shoe size of 7 or smaller is: 23 18 .
Explanation
Understand the problem and provided data We are given a table that shows the shoe sizes of 23 students and their corresponding frequencies. We need to find the probability of two events: (a) A student has a shoe size of 8. (b) A student has a shoe size of 7 or smaller.
Calculate the probability of shoe size 8 (a) To find the probability that a student has a shoe size of 8, we need to divide the number of students with shoe size 8 by the total number of students. From the table, we see that there are 4 students with shoe size 8, and there are a total of 23 students. Therefore, the probability is: Total number of students Number of students with shoe size 8 = 23 4 So, the probability that a student has a shoe size of 8 is 23 4 .
Calculate the probability of shoe size 7 or smaller (b) To find the probability that a student has a shoe size of 7 or smaller, we need to add the number of students with shoe sizes 5, 6, and 7, and then divide by the total number of students. From the table, we see that there are 2 students with shoe size 5, 11 students with shoe size 6, and 5 students with shoe size 7. Therefore, the probability is: Total number of students Number of students with shoe size 5, 6, or 7 = 23 2 + 11 + 5 = 23 18 So, the probability that a student has a shoe size of 7 or smaller is 23 18 .
State the final answer (a) The probability that a student has a shoe size of 8 is 23 4 .
(b) The probability that a student has a shoe size of 7 or smaller is 23 18 .
Examples
This type of probability calculation is useful in many real-world scenarios. For example, a store owner might use this to determine the likelihood of needing to restock certain shoe sizes based on customer data. Similarly, a teacher could use this to understand the distribution of student ages in a class. In general, understanding the probability of different events can help in making informed decisions in various fields, from business to education to healthcare.
