Question

1. in a class of 50 students there are 31 who like math class and 22 that like science class. if 7 students like both, how many students like neither subject? a) 2 b) 6 c) 8 d) 4 15. using the same venn diagram, what is the probability a student will like only math? a) \\( \frac { 12 } { 25 } \\) b) \\( \frac { 24 } { 50 } \\) c) \\( \frac { 7 } { 50 } \\) d) \\( \frac { 19 } { 50 } \\) 16. 460 students were surveyed about their class schedule. how many boys are in math class? a) cannot be determined from the given information b) 98 c) 40 d) 127 17. using the same table, how many total students are in math class? a) 55 b) cannot be determined from the given information c) 153 d) 95 18. using the same table, how many students are boys? a) 231 b) 265 c) 167 d) cannot be determined from the given information

Explanation:

Step1: Find the number of students who like at least one subject

Use the principle of inclusion - exclusion. The formula for \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\), where \(n(A)\) is the number of students who like math (\(n(A) = 31\)), \(n(B)\) is the number of students who like science (\(n(B)=22\)), and \(n(A\cap B)\) is the number of students who like both (\(n(A\cap B) = 7\)).

$$n(A\cup B)=31 + 22-7=46$$

Step2: Find the number of students who like neither subject

Let the total number of students be \(N = 50\). The number of students who like neither subject \(x=N - n(A\cup B)\)

$$x=50 - 46=4$$

Step1: Find the number of students who like only math

The number of students who like only math \(y=n(A)-n(A\cap B)\). Since \(n(A) = 31\) and \(n(A\cap B)=7\), then \(y = 31-7=24\)

Step2: Calculate the probability

The probability \(P\) that a student likes only math is given by the formula \(P=\frac{\text{Number of students who like only math}}{\text{Total number of students}}\). The total number of students \(N = 50\).

$$P=\frac{24}{50}$$

Step1: Analyze the table for question 16

The table only gives the number of girls in math (\(55\)) and no information about the number of boys in math (the "Math" row for "Boys" is empty).

Step1: Analyze the table for question 17

The table only gives the number of girls in math (\(55\)) and no information about the number of boys in math. So, we cannot find the total number of students in math.

Answer:

d) 4