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:Step-by-step explanation: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 populationThat means total number of students being surveyed is 13+13=26 studentsThen we work out the probabilityP(One pet) = 8/26 = 4/13P(Two pets) = 1/2P(Three pets) = 3/26P( Four pets) = 2/26 = 1/13The probability distribution is shown in the table below. Let  be the number of pets and  is the probability of owning the number of pets