Each person in a representative sample of 3,337 students at two-year colleges was asked how they would
describe their household's financial situation compared to before the COVID-19 pandemic. Each person in
the sample was also asked if they have children who depend on them for care living with them. The
responses are summarized in the table.
Better than Before Same as Before Worse than Before
Children 41 300 308
No Children 212 1,509 967
Suppose one of these 3,337 two-year college students is to be selected at random.
(a) What is the probability that the selected student has children? (Round your answer to four decimal
places.)
(b) What is the probability that the selected student responded that they are better off than before the
pandemic?
(c) What is the probability that the selected student has children and reported their financial situation
was worse than before the pandemic?
(d) What is the probability that the selected student does not have children and reported that their
financial situation was the same as before the pandemic?
(e) What is the probability that the selected student does not have children and reported their financial
situation was worse than before the pandemic?
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To solve this problem, we need to use conditional probability and the given table.
(a) The probability that the selected student has children is given by the number of students with children divided by the total number of students:
P(Children) = (41 + 300 + 308) / 3337 = 649 / 3337 ≈ 0.1950.
(b) The probability that the selected student responded that they are better off than before the pandemic is given by the number of students who responded "Better than Before" divided by the total number of students:
P(Better than Before) = (41 + 212) / 3337 = 253 / 3337 ≈ 0.0758.
(c) The probability that the selected student has children and reported their financial situation was worse than before the pandemic is given by the number of students with children who responded "Worse than Before" divided by the total number of students:
P(Children and Worse than Before) = 308 / 3337 ≈ 0.0923.
(d) The probability that the selected student does not have children and reported that their financial situation was the same as before the pandemic is given by the number of students without children who responded "Same as Before" divided by the total number of students:
P(No Children and Same as Before) = 1509 / 3337 ≈ 0.4523.
(e) The probability that the selected student does not have children and reported their financial situation was worse than before the pandemic is given by the number of students without children who responded "Worse than Before" divided by the total number of students:
P(No Children and Worse than Before) = 967 / 3337 ≈ 0.2899.
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