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: Calculate the number of students who like at least one subject

Use the formula \(n(A\cup B)=n(A)+n(B)-n(A\cap B)\). Here, \(n(A) = 31\) (students who like math), \(n(B)=22\) (students who like science), and \(n(A\cap B) = 7\).

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

Step2: Calculate the number of students who like neither subject

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

$$x=50 - 46=4$$

Answer:

d) 4