A survey asked students whether they have any siblings and pets. The survey data are shown in the relative frequency table. Siblings No siblings TotalPets 0.3 0.15 0.45No pets 0.45 0.1 0.55Total 0.75 0.25 1.0Given that a student has a sibling, what is the likelihood that he or she does not have a pet?A.40%B.60%C.45%D.About 82%
Question
A survey asked students whether they have any siblings and pets. The survey data are shown in the relative frequency table. Siblings No siblings TotalPets 0.3 0.15 0.45No pets 0.45 0.1 0.55Total 0.75 0.25 1.0Given that a student has a sibling, what is the likelihood that he or she does not have a pet?A.40%B.60%C.45%D.About 82%
Solution
To solve this problem, we need to look at the conditional probability. The question is asking for the probability that a student does not have a pet given that the student has a sibling.
From the table, we can see that the total proportion of students with siblings is 0.75. Out of these, the proportion of students with siblings and no pets is 0.45.
So, the conditional probability is calculated as follows:
P(No pets | Siblings) = P(No pets and Siblings) / P(Siblings) = 0.45 / 0.75 = 0.6 or 60%
So, the answer is B. 60%.
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