Question

Taylor surveys students in one grade level who own at least one pet. She finds that 50% of the students surveyed own 2 pets, 3 students own 3 pets each, and 2 students own 4 pets each. Eight of the students in the grade own 1 pet. Considering the number of pets as the random variable, X, which of the following is the probability distribution, PX(x)?

Answer 1

A.

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Answer 2

First, we need to work out the total number of students who were being surveyed.

We know that half of the students has two pets. The rest of the students make up the other half. So, we have 3 students + 2 students + 8 students = 13 students that make half of the sample population

That means total number of students being surveyed is 13+13=26 students

Then we work out the probability
P(One pet) = 8/26 = 4/13
P(Two pets) = 1/2
P(Three pets) = 3/26
P( Four pets) = 2/26 = 1/13

The probability distribution is shown in the table below. Let $x$ be the number of pets and $P(X=x)$ is the probability of owning the number of pets