Exam 3: Probability

A study revealed that 45% of college freshmen are male and that 18% of male freshmen earned college credits while still in high school. Find the probability that a randomly chosen college Freshman will be male and have earned college credits while still in high school.

A pair of fair dice is tossed. Events A and B are defined as follows. A: {The sum of the numbers on the dice is 3} B: {At least one of the dice shows a 2} Identify the sample points in the event A ∩ B.

Your manager will assign her 10 employees to three tasks, 5 to task A, 3 to task B, and 2 to task C. If she randomly assigns employees to tasks, what is the probability that you and your best friend will be assigned to the same task?

A number between 1 and 10, inclusive, is randomly chosen. Events A and B are defined as follows. A: {The number is even} B: {The number is less than 7} Which expression represents the event that the number is even or less than 7 or both?

A sample of 350 students was selected and each was asked the make of their automobile (foreign or domestic)and their year in college (freshman, sophomore, junior, or senior). The results are Shown in the table below. What is the probability of randomly selecting a student who is in the freshman class or drives a foreign automobile?

Suppose that for a certain experiment $P ( A ) = .15 \text { and } P ( B \mid A ) = .8 \text {. Find } P ( A \cap B ) \text {. }$

The data below show the types of medals won by athletes representing the United States in the Winter Olympics. Suppose that one medal is chosen at random and the type of medal noted. gold gold silver gold bronze silver silver bronze gold silver silver bronze silver gold gold silver silver bronze bronze gold silver gold gold bronze bronze a. List the sample points for this experiment. b. Find the probability of each sample point. c. What is the probability that the medal was not bronze?

In a box of 50 markers, 30 markers are either red or black, 20 are missing their caps, and 12 markers are either red or black and are missing their caps. Are the events ʺred or blackʺ and ʺmissing capʺ dependent or independent? Explain.

An exit poll during a recent election revealed that 52% of those voting were women and 48% were men. The results also showed that 70% of the women voting favored Democratic candidates while only 40% of the men favored Democratic candidates. These poll results may be summarized as follows: P(woman)= .52 P(man)= .48 P(favored Democrats | woman)=.70 P(favored Democrats | man)= .40 a. Find P(woman and favored Democrats). b. Find P(man and favored Democrats). c. Find P(favored Democrats). d. Find P(woman | favored Democrats). e. Find P(man | favored Democrats).

Evaluate $\left( \begin{array} { l } 7 \\7\end{array} \right)$

If every sample point in event B is also a sample point in event A, then $P ( A \mid B ) = 1 .$

The accompanying Venn diagram describes the sample space of a particular experiment and events A and B. Suppose the sample points are equally likely. Find P(A)and P(B).

An experiment consists of randomly choosing a number between 1 and 10. Let A be the event that the number chosen is less than or equal to 7. List the sample points in A.

Each manager of a corporation was rated as being either a good, fair, or poor manager by his/her boss. The managerʹs educational background was also noted. The data appear below: If we randomly selected one manager from this company, find the probability that he or she has an advanced (Master's or Ph.D.) degree and is a good manager.

Find the numerical value. -A panel of coaches ranks the high school football teams in a particular state each week. The panel unanimously agrees on which five teams should comprise the top five but not on the order. Riverside High and Hillside High are among the top five. If the ranking of the top five is random, What is that probability that Riverside High will be ranked first and Hillside High will be ranked Second?

In any experiment with exactly four sample points in the sample space, the probability of each sample point is .25.

Find the numerical value. - $\mathrm { P } _ { 4 } ^ { 5 }$

The data below show the types of medals won by athletes representing the United States in the Winter Olympics. Suppose that one medal is chosen at random and the type of medal noted. gold gold silver gold bronze silver silver bronze gold silver silver bronze silver gold gold silver silver bronze bronze gold silver gold gold bronze bronze Given that the medal is not bronze, what is the probability that the medal is gold?

Suppose that for a certain experiment $P ( A ) = .37 , P ( B ) = .69$ , and $P ( A \cap B ) = .23$ . Find $P ( A \cup$ $B )$ .

If A and B are independent events, then A and B are also mutually exclusive.