A survey asked a random sample of U.S. adults about their political party affiliation and how long they thought they would survive compared to most people in their community if an apocalyptic disaster were to strike. The responses are summarized in the following two-way table.

Suppose we select one of the survey respondents at random. Which of the following probabilities is the largest?

a. P(Independent and Longer)

b. P(Independent or Not as long)

c. P(Democrat $\frac{305}{1526}=0.200=20.0\%$| Not as long)

d. P(About as long $\left|\frac{305}{1526}=0.200=20.0\%\right|$| Democrat)

e. P(About as long)

We have to tell probabilities is the largest.

The table has $360$Democrats (since$360$is indicated in the row "Total" and the column "Democrat" of the given table), with $169$of the $360$Democrats projected to live about as long as the rest of the population (since$168$is mentioned in the row "About as long" and in the column "Democrat" of the given table).

The table comprises $998$U.S. adults in total (which is stated in the bottom right corner of the table), with $416$of those $998$U.S. adults being Independent and anticipated to live about as long as the average American adult (since $416$is mentioned in the row "About as long" and in the column "Total" of the given table).

$P(\text{About as long}\mid \text{Democrat})=\frac{\#\text{of favorable outcomes}}{\#\text{of possible outcomes}}=\frac{169}{360}\approx 0.4694$