Exam 8: Probability

The phrase "Dogs of the Dow" refers to the stocks listed in the Dow with the highest dividend yield. This table shows the top ten stocks of the "Dogs of the Dow" list. If you selected two of these stocks at random, what is the probability that both the stocks in your selection had yields of 3.5% or more Symbol Company Yield SBC SBC Communications 5.48\% GM General Motors 5.48\% MRK Merck 5.42\% MO Altria 4.55\% VZ Verizon 4.32\% JPM JP Morgan Chase 3.78\% C Citigroup 3.64\% PFE Pfizer 3.12\% DD DuPont 2.98\% GE General Electric 2.46\%

Determine whether the given information is consistent with a probability distribution. If not, say why. ​ $P ( A ) = 0.7$ ; $P ( B ) = 0$ ; $P ( A \cap B ) = 0$

A dodecahedral die has 12 faces, numbered 1 - 12. If the die is weighted in such a way that 2 is twice as likely to be facing up as 1, 3 is three times as likely to be facing up as 1, and so on, what is the probability that 4 will land facing up

Use Bayes' theorem or a tree diagram to calculate the indicated probability. Round the answer to four decimal places. $Y _ { 1 }$ , $Y _ { 2 }$ , $Y _ { 3 }$ form a partition of S. $P \left( X \mid Y _ { 1 } \right) = 0.2$ , $P \left( X \mid Y _ { 2 } \right) = 0.3$ , $P \left( X \mid Y _ { 3 } \right) = 0.5$ , $P \left( Y _ { 1 } \right) = 0.3$ , $P \left( Y _ { 2 } \right) = 0.4$ . Find $P \left( Y _ { 2 } \mid X \right)$ .

Determine whether the given events A and B are independent, mutually exclusive, or neither. ​ A: Your new skateboard design is a success. B: There is life in the Andromeda Galaxy. ​

You are given a transition matrix P. Find the steady-state distribution vector. $P = \left[ \begin{array} { c c c } 0.3 & 0 & 0.7 \\1 & 0 & 0 \\0 & 0.6 & 0.4\end{array} \right]$

In 2004, 45.4% of all light vehicles were cars, 27.3% were pickups, and 27.3% were SUVs. The probability that a severe side-impact crash would prove deadly to a driver depended on the type of vehicle he or she was driving at the time, as shown in the table. What is the probability that the victim of a deadly side-impact accident was driving an SUV Please, round your answer to four decimal places. Light Truck 210 SUV 371 Cars 1.000 The probability is __________.

Write down the transition matrix associated with the given state transition diagram. ​ ​ $A = \frac { 3 } { 4 }$ , $B = \frac { 1 } { 4 }$ , $C = \frac { 3 } { 4 }$ , $D = \frac { 1 } { 4 }$ , $E = \frac { 3 } { 4 }$ , $H = \frac { 1 } { 4 }$

According to a study conducted by the Harvard School of Public Health, a driver who was wearing a seatbelt was 31% more likely to be killed in an accident if the car had an air bag that deployed than if it did not. Airbags deployed in 25% of all accidents. For a driver wearing a seatbelt, what is the probability that the airbag deployed in an accident in which the driver was killed (Round your answer to two decimal places.)

Let W be the event that you will use the website tonight, Q be the event that your math grade will improve, and E be the event that you will use the website every night. Express the following event in symbols. "Either your math grade will improve, or you will use the website tonight, but not every night."

Two dice are rolled. Could there be two mutually exclusive events that both contain outcomes in which the numbers facing up add to 10 If yes, give an example.

This table shows the performance of the selection of 100 stocks after one year. (Take S to be a set of all stocks represented in the table.) Use symbols to describe the event that Internet stock did not increase. How many elements are there in this event Companies Pharmaceutical P Electronic E Internet I Total Increased V 15 10 15 40 Unchanged N 15 5 10 30 Decreased D 10 5 15 30 Total 40 20 40 100

The following table shows the results of a survey of 410 authors by a (fictitious) publishing company: New Authors Established Authors Total Successful 40 50 90 Unsuccessful 130 190 320 Total 170 240 410 ​ An author is chosen at random. Compute the estimated probability of the event that the author is successful.

Suppose that a monkey sits at the computer keyboard and randomly strikes the 26 letter keys and the space bar. Find the probability that its first 65 characters (including spaces) will be "All the world is a stage and all the men and women merely players."

Suppose two dice (one green, one red) are rolled. Consider the following events. A: The red die shows 2. B: The numbers add to 6. C: At least one of the numbers is 2. D: The numbers do not add to 10. Express the given event in symbols. "The numbers do not add to 6."

You are given a transition matrix P. Find the steady-state distribution vector. ​ $P = \left[ \begin{array} { c c c } 0.4 & 0 & 0.6 \\1 & 0 & 0 \\0 & 0.4 & 0.6\end{array} \right]$

According to the New York Times/CBS poll of March, 2005, 46% agreed that Social Security taxes should be raised if necessary to keep the system afloat, and 42% agreed that it would be a good idea to invest part of their Social Security taxes on their own. What is the largest percentage of people who could have agreed with at least one of these statements The largest percentage is __________%. What is the smallest percentage of people who could have agreed with at least one of these statements The smallest percentage is __________%.

In a hand of poker, a player is dealt 5 cards at random from a deck of 52. Below is a list of poker hands ranked in order from the highest to the lowest, along with a description and example of each hand. Use the table to answer the problem. What is the probability of being dealt a full house Round your answer to five decimal places.

According to the New York Times/CBS poll of March, 2005, 77% agreed that it should be the government's responsibility to provide a decent standard of living for the elderly, and 44% agreed that it would be a good idea to invest part of their Social Security taxes on their own. What is the smallest percentage of people who could have agreed with both statements The smallest percentage is __________%. What is the largest percentage of people who could have agreed with both statements ? The largest percentage is __________%.

In fall 2003, UCLA admitted 24% of its California resident applicants, 22% of its applicants from other U.S. states, and 18% of its international student applicants. Of all its applicants, 87% were California residents, 9% were from other U.S. states, and 4% were international students. What percentage of all admitted students were California residents (Round your answer to the nearest 1%.) ?