91Ó°ÊÓ

Why is the following not a probability model? $$ \begin{array}{lc} \text { Color } & \text { Probability } \\ \hline \text { Red } & 0.3 \\ \hline \text { Green } & -0.3 \\ \hline \text { Blue } & 0.2 \\ \hline \text { Brown } & 0.4 \\ \hline \text { Yellow } & 0.2 \\ \hline \text { Orange } & 0.2 \\ \hline \end{array} $$

The probability that a randomly selected individual in the United States 25 years and older has at least a bachelor's degree is \(0.094 .\) The probability that an individual in the United States 25 years and older has at least a bachelor's degree, given that the individual lives in Washington \(\mathrm{DC},\) is, \(0.241 .\) Are the events "bachelor's degree" and "lives in Washington, DC," independent?

Why is the following not a probability model? $$ \begin{array}{lc} \text { Color } & \text { Probability } \\ \hline \text { Red } & 0.1 \\ \hline \text { Green } & 0.1 \\ \hline \text { Blue } & 0.1 \\ \hline \text { Brown } & 0.4 \\ \hline \text { Yellow } & 0.2 \\ \hline \text { Orange } & 0.3 \end{array} $$

Which of the following numbers could be the probability of an event? $$ 0,0.01,0.35,-0.4,1,1.4 $$

What is the probability of obtaining five heads in a row when flipping a fair coin? Interpret this probability.

What is the probability of obtaining 4 ones in a row when rolling a fair, six- sided die? Interpret this probability.

Drawing a Card Suppose that a single card is selected from a standard 52 -card deck. What is the probability that the card drawn is a king? Now suppose that a single card is drawn from a standard 52 -card deck, but we are told that the card is a heart. What is the probability that the card drawn is a king? Did the knowledge that the card is a heart change the probability that the card was a king? What term is used to describe this result?

About \(13 \%\) of the population is left-handed. If two people are randomly selected, what is the probability that both are left-handed? What is the probability that at least one is right-handed?

According to Nate Silver, the probability of a senate candidate winning his/her election with a \(5 \%\) lead in an average of polls with a week until the election is \(0.89 .\) Interpret this probability.

According to the U.S. National Center for Health Statistics, \(0.15 \%\) of deaths in the United States are 25 - to 34-year-olds whose cause of death is cancer. In addition, \(1.71 \%\) of all those who die are \(25-34\) years old. What is the probability that a randomly selected death is the result of cancer if the individual is known to have been \(25-34\) years old?