i need help with this attached homework. i need help with this attached homework

 

 

Homework 4
Due Sunday, Sept. 18 at midnight
I don’t require you to show your work, but I can’t give you any partial
credit for wrong answers if you don’t show how you got your solutions.
1. Your classmate tells you she has three children, but you do not know
the gender of her children.
a. Using B for boy and G for girl, write out the sample space for all
of the possibilities of genders for her children. (There should be
8 possibilities!)
b. What is the probability that she has two boys?
c. What is the probability that she has at least two boys?
d. What is the probability that she had two boys and then a girl?
2. Suppose a high school has 254 freshmen, 238 sophomores, 197
juniors, and 213 seniors. If you randomly select one student from this
high school, what is the probability the student is not a freshman?
3. Suppose in a small town in Russia, the probability of having sunny
weather on a given day is 0.65, and the probability of having cold
weather is 0.8. The probability of the weather being both sunny and
cold is 0.6.
a. What is the probability of having sunny or cold weather?
b. If a resident of this town looks outside and sees that it is sunny,
what is the probability that it is cold outside?
c. In words, explain why the probability in b is different from the
given probability of being both sunny and cold.
d. If a resident of this town sees on the news that it is cold outside,
what is the probability that it is sunny?
4. The following table is based on data from “Helmet Use and Risk of
Head Injuries in Alpine Skiers and Snowboarders,” by Sullheim, et al.,
Journal of the American Medical Association, Vol. 295, No. 8).
Wore Helmet
No Helmet Head Injuries
96
480 Not Injured
656
2330 a. If one of the subjects is randomly selected, find the probability of
selecting someone with a head injury.
b. If one of the subjects is randomly selected, find the probability of
selecting someone who wore a helmet.
c. If one of the subjects is randomly selected, find the probability of
selecting someone who did not wear a helmet or was not injured. d. If one of the subjects is randomly selected, find the probability of
selecting someone who did not wear a helmet and was not
injured.
e. If two different study subjects are randomly selected, find the
probability that they both had head injuries.
f. If one of the subjects is randomly selected, find the probability of
selecting someone who was not injured, given that the subject
wore a helmet.
5. In a basketball arena, 70% of the fans are rooting for the home team. 25% of the fans are wearing blue. 20% of the fans are wearing blue and are rooting for the away
team. Of the fans rooting for the away team, 67% are wearing blue.
a. Are the events of wearing blue and rooting for the away team
independent? How do you know?
b. Are they mutually exclusive? How do you know?
Hint: there are equations that must be true for events to be
independent or mutually exclusive – read the opening pages of
Section 3.2 in the textbook.
6. Use counting rules to answer the following problems.
a. Find the number of different ways that the nine players on a
baseball team can line up for the National Anthem.
b. A political strategist must visit state capitols, but she has time to
visit only 3 of them. Find the number of different possible routes.
c. A statistics professor owns a safe in which he stores all of his
great ideas for the next edition of his textbook. The safe
combination consists of four different numbers between 0 and
99. If another author breaks in and tries to steal these ideas,
what is the probability that he or she will get the correct
combination on the first attempt? Assume that the numbers are
randomly selected.
d. How many 5-card draw poker hands are there? In other words, in
how many ways can I select 5 cards from a deck of 52 cards,
where the order in which they are dealt doesn’t matter?
e. The Florida Lotto game is typical of state lotteries. You must
select six different numbers between 1 and 53. You win the
jackpot if the same six numbers are drawn in any order. Find the
probability of winning the jackpot.
f. In horse racing, a trifecta is a bet that the first three finishers in a
race are selected, and they are selected in the correct order.
Find the number of different possible trifecta bets in a race with
ten horses. EXTRA CREDIT:
7. Suppose you own a sports-themed burger shop called The Yard. It is
very popular with the local high school, St Matthew’s School for Boys.
However, it is even more popular now that your new employee for the
summer, Kelli, has started making her famous chocolate milkshakes for
your customers. You’ve estimated that when a potential customer
walks by and sees that Kelli is working, 9 times out of 10 they come in
for a milkshake. A group of 4 students from St Matthew’s have just
gotten off the bus.
a. Assuming that each student thinks independently, what is the
probability that Kelli’s milkshake brings all the boys to The Yard?
b. It is probably not a good assumption that teenage boys think
independently of each other. Assume instead that if any boy
chooses to come, they all do. Now what is the probability that
Kelli’s milkshake brings all the boys to The Yard?
at least one boy comes ∈¿
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Hint:
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