Question

1. in a class of 40 students there are 25 who like math class and 20 that like science class. if 7 students like both fill in the following venn diagram. (make sure to label)

a. how many students like neither subject?
b. what is the probability a student will like only math?

Explanation:

Step1: Calculate students who like only math

Number of students who like only math = Students who like math - Students who like both
$25 - 7=18$

Step2: Calculate students who like only science

Number of students who like only science = Students who like science - Students who like both
$20 - 7 = 13$

Step3: Calculate students who like neither

Total students = Students who like only math + Students who like only science + Students who like both + Students who like neither
$40=18 + 13+7+N$
$N=40-(18 + 13+7)$
$N=2$

Step4: Calculate probability of liking only math

Probability $P=\frac{\text{Number of students who like only math}}{\text{Total number of students}}$
$P=\frac{18}{40}=\frac{9}{20}=0.45$

Answer:

a. $2$
b. $\frac{9}{20}$ or $0.45$