Quiz 6 – Math 163
Spring, 2014
Name:
Show all your work to receive full credit. If you have an answer and no work I can award no partial
credit if your answer is incorrect. If you show your work, partial credit can be awarded when merited.
Some probability rules for events A and B:
1.
2.
3.
4.
If A and B are disjoint, 𝑷(𝑨 or 𝑩) = 𝑷(𝑨) + 𝑷(𝑩)
𝑨𝑪 is the event that A does not occur. 𝑷(𝑨𝑪 ) = 𝟏 − 𝑷(𝑨)
𝐈f A and B are independent, 𝑷(𝑨 and 𝑩) = 𝑷(𝑨)𝑷(𝑩) and 𝑷(𝑩|𝑨) = 𝑷(𝑩)
𝐅𝐨𝐫 any two events A and B, 𝑷(𝑨 or 𝑩) = 𝑷(𝑨) + 𝑷(𝑩) − 𝑷(𝑨 and 𝑩)
5. 𝐖𝐡𝐞𝐧 𝑷(𝑨) > 0, the conditional probability of B given A is 𝑷(𝑩|𝑨) =
𝑷(𝑨 and 𝑩)
𝑷(𝑨)
1. Nick Johnson had a 78.1% free throw percentage for the 2013 – 2014 UA Men’s Basketball
season. Let 𝑆 be the number of successful free throws that occur for the three free throws
executed by Johnson.
A. What is the probability that 𝑆 = 1?
B. Find the distribution of 𝑆 and all the associated probabilities.
2. Internet sites often vanish or move, so that references to them cannot be followed. Within 2
years after publication, 13% of Internet sites referenced in major scientific journals are lost. If a
paper contains 6 Internet references, what is the probability that all 6 are still good two years
later? What specific assumption did you make to calculate this probability?
3. Of all college degrees awarded in the United States, 50% are bachelor’s degrees, 41% are earned
by men and 24% are bachelor’s degrees earned by men.
A. Make a Venn diagram (fill in all the appropriate probabilities) and use it to answer the
following questions.
B. What is the probability that a randomly chosen person is a female without a bachelor’s
degree?
C. What is the probability that a randomly chosen person is a woman with a bachelor’s
degree?
D. What is the probability that a randomly chosen person is a male or has a bachelor’s degree?
E. Are being a male and getting a bachelor’s degree independent events? Show work.
4. Two cards are selected in sequence from a standard deck. If the first card you draw is a king,
find the probability that the second card is a queen.
5. A company retains a psychologist to assess whether job applicants are suited for assembly – line
work. The psychologist classifies applicants as one of 𝑊 (well suited), 𝑀 (marginal), or 𝑁 (not
suited). The company is concerned about the event 𝐿 that an employee leaves the company
within a year of being hired. Data on all people hired in the past five years give the following
probabilities:
𝑃(𝑊) = 0.4
𝑃(𝑊 and 𝐿) = 0.1
A.
𝑃(𝑀) = 0.3
𝑃(𝑀 and 𝐿) = 0.1
𝑃(𝑁) = 0.3
𝑃(𝑁 and 𝐿) = 0.2
Sketch a Venn diagram of the 4 events and mark on the diagram the probabilities of all
combinations of psychological assessment and leaving (or not) within a year.
B. Find 𝑃(𝐿).
6. More than 15,000 US medical school seniors applied to residency programs in 2009. Of those
93% were matched with residency programs. Eighty-two percent of the seniors matched with
residency programs were matched with one of their top three choices.
A. Find the probability that a randomly selected senior was matched with a residency program
and it was one of the senior’s top three choices.
B. Find the probability that a randomly selected senior who was matched with a residency
program did not get matched with one of the senior’s top three choices.
7. A player serving in tennis has two chances to get a serve into play. If the first serve is out, the
player serves again. If the second serve is also out, the player loses the point. Four years of
data collected at Wimbledon show the follow probabilities: the probability that the first serve is
in is 0.59, if the first serve is in, the probability they win the point is .73, if the first serve is out,
the probability that the second serve is in is 0.86, and if the first serve is out and the second
serve is in, the probability that they win the point is 0.59.
A. Write these probabilities using the proper conditional probability notation.
B. Make a tree diagram for the results of the two serves and the outcome (win or lose) of the
point. Label the probabilities on the branches.
C. Use your tree to find the probability that the server wins the point.