14. in a class of 50 students there are 31 who like math class and 22 that like science class. if 7 students…

14. 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
Answer
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