Question

a principal of a school with 484 students collected information about how many of the students wear glasses.

1. complete the table
2. how many boys sometimes wear glasses?
3. how many students wear glasses some of the time?
4. how many students never wear glasses?
5. what is the probability that a student is a girl that never wear glasses?
6. what is the probability a student chosen at random is a boy?
7. what is the probability that a student always wear glasses?

Explanation:

Step1: Calculate boys' total

Total number of boys = \(40 + x+ 161\). Total number of students is \(484\). Number of girls is \(36 + 55+144=235\). So number of boys \(=484 - 235 = 249\). Then \(40+x + 161=249\), \(x=249-(40 + 161)=48\) (number of boys who sometimes wear glasses)

Step2: Calculate students who sometimes wear glasses

Students who sometimes wear glasses \(=48 + 55=103\)

Step3: Calculate students who never wear glasses

Students who never wear glasses \(=161+144 = 305\)

Step4: Calculate probability that a student is a girl that never wear glasses

Number of girls that never wear glasses is \(144\). Probability \(P=\frac{144}{484}=\frac{36}{121}\)

Step5: Calculate probability that a student is a boy

Number of boys is \(249\). Probability \(P=\frac{249}{484}\)

Step6: Calculate probability that a student always wear glasses

Number of students who always wear glasses \(=40 + 36=76\). Probability \(P=\frac{76}{484}=\frac{19}{121}\)

Answer:

1. Boys' total: \(249\); Girls' total: \(235\); Total - always: \(76\); Total - sometimes: \(103\); Total - never: \(305\); Grand - total: \(484\)
2. \(48\)
3. \(103\)
4. \(305\)
5. \(\frac{36}{121}\)
6. \(\frac{249}{484}\)
7. \(\frac{19}{121}\)