Name:

  1. The probability that a U.S. household subscribes to Netflix is 20%. The probability that a U.S. household subscribe to Disney+ is 10%. The probability that a household subscribes to Netflix or Disney+ is 24%. Use this information to answer the following questions.
  1. What is the probability that a household subscribes to Netflix and Disney+?

\[ \begin{align*} P(N \cap D+) & = P(N) + P(D+) - P(N \cup D+) \\ & = 6\% \end{align*} \]

  1. What is the probability that that a household does not subscribe to Netflix?

\(P(N') = 1-0.2 = 80\%\)

  1. What is the probability that a household doesn’t subscribe to any subscription service?

\(1 - P(N \cup D+) = 76\%\)

  1. Given that a house hold subscribes to Netflix, what is the probability that the household also subscribes to Disney+?

\[\begin{align*} P(D+|N) & = \frac{P(N \cap D+)}{P(N)} \\ & = \frac{0.06}{0.2} \\ & = 30\% \end{align*} \]

  1. Due to rising health insurance costs, 37 million people in the United States go without health insurance. Sample data representative of the national health insurance coverage are available in the data set EC245-Q5-Health Care
No Yes Sum
18 to 34 0.085 0.375 0.46
35 & Older 0.065 0.475 0.54
Sum 0.150 0.850 1.00

  1. Develop a joint probability table for these data. Paste the table into this document.

  2. What do the marginal probabilities tell you about the age of the U.S. population?

The 18-34 age group consists of 46% of the sample while the 35 and older group consists of 54% of the sample. There are slightly more older people than younger people in the group.

  1. What is the probability that a randomly selected individual does not have health insurance coverage?

There is a 15% chance that a randomly selected individual does not have health insurance.

  1. Given the individual is between the ages of 18 and 34, what is the probability that the individual does not have health insurance coverage?

\[\begin{align*} P(No Ins|18-34) & = \frac{0.085}{0.46} \\ & = 18.5\% \end{align*} \]

  1. Given the individual is age 35 or older, what is the probability that the individual does not have health insurance coverage?

\[\begin{align*} P(No Ins|35-Older) & = \frac{0.065}{0.54} \\ & = 12\% \end{align*} \]

  1. Given the individual does not have health insurance, what is the probability that the individual is in the 18-34 group?

\[\begin{align*} P(18-34|No Ins) & = \frac{0.085}{0.15} \\ & = 56.7\%\ \end{align*} \]

  1. What does the probability information tell you about health insurance coverage in the United States?

This suggests that younger people are less likely to have insurance. Of the individuals who do not have insurance, 57% are in the 18-34 group. Of young people, 18.5% do not have insurance.