Question

In a school, there are 120 students. 20 students have no pets, 46 have only 1 pet, 33 have 2 pets, and 21 have at least 3 pets. If a student is picked at random, what is the probability that the student has at least 1 pet?

• A. $\frac{1}{6}$
• B. $\frac{2}{6}$
• C. $\frac{4}{6}$
• D. $\frac{5}{6}$

Answer 1

The correct option is D $\frac{5}{6}$

$P\left(\text{student has at least one pet}\right)=1-P\left(\text{student has no pets}\right)$

$P\left(\text{student has no pets}\right)=\frac{20}{120}=\frac{1}{6}$

$P\left(\text{student has at least one pet}\right)=1-\frac{1}{6}=\frac{5}{6}$


$\underset{–}{AlternateSolution:}$

Given:
Total number of students = 120
Number of students with exactly 1 pet = 46
Number of students with exactly 2 pets = 33
Number of students with exactly 3 pets = 21

To find: P(at least 1 pet)
Number of students with at least 1 pet = 46 + 33 + 21 = 100

P(at least 1 pet) $=\frac{100}{120}=\frac{5}{6}$