**Problem number 5#
Eleven of the 50 **

digital recorders (DVRs) in an inventory are known to be defective. What is the
probability you randomly select an item that is not defective? The probability
is ---- (Do not round).

**problem # 6 Identify
the sample space of the probability experiment and determine the number of
outcomes in the sample space. Randomly choosing an odd number between 1 and 9,
inclusive The sample space is---- (Use a comma to separate answers as needed.
Use ascending order.) so there are ---- outcomes in the sample space. **

**problem#7. A software
company is hiring for two positions: a software development engineer and a
sales operations manager. How many ways can these positions be filled if there
are 19 people applying for the engineering position and 18 people applying for
the managerial position? The position can be filled in ---- ways. **

**problem#9. Consider a
company that selects employees for random drug tests. The company uses a
computer to randomly select employees numbers that range from 1 to 5839. Find
the probability of selecting a number less than 1000. Find the probability of
selecting a number greater than 1000. The probability of selecting a number
less than 1000 is--(Round to three decimal places as needed.) The probability
of selecting a number greater than 1000 is---(Round to three decimal places as
needed.) **

**problem #10. Consider
a company that selects employees for random drug tests. The company uses
computer to randomly select employee numbers that range from 1 to 6282. Find
the probability of selecting a number less than 1000. Find the probability of
selecting a number greater than 1000. The probability of selecting a number
less than 1000 is--- round to three decimal places as needed. The probability
of selecting a number greater than 1000 is--- round to three decimal places as
needed. **

**problem #11. A
probability experiment consists of rolling a eight sided die and spinner shown
at the right. The spinner is equally likely to land on each color. Use a tree
diagram to find the probability of the given event. Then tell whether the event
can be considered unusual. Event: rolling a number less than 3 and the spinner
landing on yellow the probability of the event is --- ( type an integer or
decimal rounded to three decimal places as needed.) Can the event be considered
unusual? **

**problem #12. Use the
frequency distribution, which shows the responses of a survey of college
students when asked, "How often do you wear a seat belt when riding in a
car driven by someone else?" Find the following probabilities of responses
of college students from the survey chosen at random. Response -- Never with
the frequency of 117, rarely-- frequency 344, sometimes-- frequency of 569,
most of the time with the frequency of 1372, always with the frequency of 2591,
complete the table below for the response and the probability **

**1. never is response
and the probability would be--- round to the nearest thousandth as needed. **

**2. response is rarely
and the probability would be--- round to the nearest thousandth as needed. **

**3. response is
sometimes and the probability would be--- round to the nearest thousandth as
needed 4. response is most of the time and the probability would be--- round to
the nearest thousandth as needed. 5. response is always and the probability
would be--- round to the nearest thousandth as needed. **

**problem #13. Use the
pie chart at the right, which shows the number of tulips purchased from a
nursery. Find the probability that a tulip bulb chosen at random is red the red
tulip bulbs are 30 the probability that a tulip bulb chosen at random is red
is--- (do not round). **

**problem#14. Use the
pie chart at the right, which shows the number of workers (in thousands) by
industry for a certain country. Find the probability that a worker chosen at
random was not employed in the mining and construction
industry. Agriculture, forestry, fishing and hunting 2981, services
115,861, manufacturing 16,055, and mining and construction 11,103. The
probability is---.(round to three decimal places as needed.) **

**problem #15. In
gambling, the chances of winning are often written in terms of odds rather than
probabilities. The odds of winning is the ratio of the number of successful
outcomes to the number of unsuccessful outcomes. The odds of losing is the
ratio of the number of successful outcomes is 2 and the number of unsuccessful
outcomes is 3, the odds of winning are 2:3 (read "2 to"3) or 2/3.
(Note: If the odds of winning are 2/3, the probability of success is 2/5.) The
odds of an event occurring are 5:1. Find (a) the probability that the event
will occur and (b) the probability that the event will not occur. The
probability that the event will occur is---. (type an integer or decimal
rounded to the nearest thousandth as needed.) The probability that the event
will not occur is---(type an integer od decimal rounded to the nearest
thousandth as needed.) **

**problem#16. The
chances of winning are often written in terms of odds rather than
probabilities. The odds of winning is the ratio of the number of successful
outcomes to the number of unsuccessful outcomes. The odds of losing is the
ratio of the number of unsuccessful outcomes is 2 and the number of
unsuccessful outcomes is 3, the odds of winning are 2:3 (read "2 to
3") or 2-3. A card is picked at random from a standard deck of 52 playing
cards. Find the odds that it is a 2 of spades. The odds that it is a 2 of
spades are---:--- (Simplify your answer). **

**problem**

** #17. In the general population, one women in
eight will develop breast cancer. Research has shown that 1 women in 650
carries a mutation of the BRCA gene. Eight out of 10 women with this mutation
develop breast cancer. (a) Find the probability that a random selected woman
will develop breast cancer given that she has a mutation of the BRCA gene. The
probability that a randomly selected woman will develop breast cancer given
that she has a mutation of the BRCA gene is---(round to one decimal place as
needed.) (b) Find the probability that a randomly selected woman will carry the
mutation of the BRCA gene and will develop breast cancer. The probability that
a randomly selected woman will carry the gene mutation and develop breast
cancer is ----(round to four decimal places as needed.) problem# 18. Suppose
80% of kids who visit a doctor have a fever, and 35% of kids with a fever have
sore throats. What's the probability that a kid who goes to the doctor has a
fever and a sore throat? the probability is--- (round to three decimal places
as needed). problem#19. According to Bayes' Theorem, the probability of event
A, given that event B, as occurred, is as follows. P( A| B)= P(A) . P(B|A) over
P(A). P(B|A)+ P(A') . P(B|A') Use Bayes' Theorem to find P(A|B) using the
probabilities shown below. P(A)=2/3, P(A') =1/3, P(B|A)=1/10, and P(B|A')=1/2 The
probability of event A, given that event B has occurred, is P(A|B)=---- (round
to the nearest thousandth as needed). **

**problem # 20.
Determine the probability that at least 2 people in a room of 9 people share
the same birthday, ignoring leap years and assuming each birthday is equally
likely, by answering the following questions: (a). the probability that 9
people have different birthdays is---(round to four decimal places as needed).
(b) the probability that at least 2 people share a birthday is--- (round to
four decimal places as needed). **

**problem 21. By
rewriting the formula for the Multiplication Rule, you can write a formula for
finding conditional probabilities. The conditional probability of event B
occurring, given that event A has occurred, is P(B|A)= P(A and B)/ P(A). Use
the information below to find the probability that a flight arrives on time
given that it departed on time. The probability that an airplane flight departs
on time is 0.91, the probability that a flight arrives on time is 0.88, the
probability that a flight departs and arrives on time is 0.81, the probability
that a flight arrives on time given that it departed on time is----(round to
the nearest thousandth as needed) **

**problem #25 The table
below shows the results of a survey that asked 2864 people whether they are
involved in any type of charity work. A person is selected at random from the
sample. Complete parts (a) through (c). frequently for male---225, for female
206 total for frequently is 431. occasionally for male is 456, female is 440
total is 896, for not at all male is 796, female is 741 total for this one is
1537, totals for male 1477, female1387 and the total is 2864, (a). Find
the probability that the person is frequently or occasionally involved in
charity work. P(begin frequently involved or being occasionally
involved)=---(round to the nearest thousandth as needed for all of them.) (b).
Find the probability that the person is female or not involved in charity work
at all. P(being female or not being involved)=--- (c) Find the probability that
the person is male or frequently involved in charity work. P(being male or
being frequently involved)=---(d) Find the probability that the person is
female or not frequently involved in charity work. P(being female or not frequently
involved)=---(e). Are the events "being female" and "being
frequently involved in charity work" mutually exclusive? Explain. **

**problem # 26.
Evaluate the given expression and express the result using the usual format for
writing numbers (instead of scientific notation). 56P2=-- **

**problem # 27. Perform
the indicated calculation is 6P3/10P4=--- (round to four decimal places as
needed). **

**problem # 28. Perform
the indicated calculation. 9C3/13C3=---(round to the nearest thousandth as
needed). **

**problem #30. Outside
a home, there is a 9-key keypad with letters A,B,C,D,E,F,G,H, and I that can be
used to open the garage if the correct nine letter code is entered. Each key
may be used only once. How many codes are possible? The number of possible code
is----. **

**problem #31. A golf
course architect has six linden trees, four white birch trees, and two bald
cypress trees to plant in a row along a fairway. In how many ways can the
landscaper plant the trees in a row, assuming that the trees are evenly spaced?
The trees can be planted in --- different ways. **

**problem # 32. Shuttle
astronauts each consume an average of 3000 calories per day. One meal normally
consist of a main dish, a vegetable dish, and two different desserts. The
astronauts can choose from 10 main dishes, 7 vegetable dishes, and 12 desserts.
How many different meals are possible? The number of different meals possible
is----.**

**problem #33. A basket
contains 9 eggs, 3 of which are cracked. If we randomly select 4 of the eggs
for hard boiling what is the probability of the following events?( A.) All
cracked eggs are selected. (B). None of the cracked eggs are selected. (C). Two
of the cracked eggs are selected. (a). the probability that none of the cracked
eggs are selected is---- (b). the probability that none of the cracked eggs are
selected is---- (c) the probability that two of the cracked eggs are selected
is--- (Round all of them to four decimal places as needed.)**