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Unformatted text preview: Math 17C (Spring 2007)
Kouba
Exam 3 Please PRINT your name here : _________________________________________________________ __
Your Exam ID Number __________ __ 1. PLEASE DO NOT TURN THIS PAGE UNTIL TOLD TO DO SO. 2. IT IS A VIOLATION OF THE UNIVERSITY HONOR CODE TO, IN ANY
WAY, ASSIST ANOTHER PERSON IN THE COMPLETION OF THIS EXAM. IT IS
A VIOLATION OF THE UNIVERSITY HONOR CODE TO COPY ANSWERS FROM
ANOTHER STUDENT’S EXAM. IT IS A VIOLATION OF THE UNIVERSITY HONOR
CODE TO HAVE ANOTHER STUDENT TAKE YOUR EXAM FOR YOU. PLEASE
KEEP YOUR OWN WORK COVERED UP AS MUCH AS POSSIBLE DURING THE
EXAM SO THAT OTHERS WILL NOT BE TEMPTED OR DISTRACTED. THANK YOU FOR YOUR COOPERATION. 3. No notes, books, or classmates may be used as resources for this exam. YOU MAY
USE A CALCULATOR ON THIS EXAM. 4. Read directions to each problem carefully. Show all work for full credit. In most
cases, a correct answer with no supporting work will NOT receive full credit. What you
write down and how you write it are the most important means of your getting a good
score on this exam. Neatness and organization are also important. 5. Make sure that you have 7 pages, including the cover page.
6. You will be graded on proper use of limit, derivative, and integral notation. 7. You have until 9:52 a.m. sharp to ﬁnish the exam. 1.) Let sample space 52 = {a, b, c, d, e, f, g, h} with all outcomes equally likely . Let events
A = {a,b,c,d}, B = {c,d, e, f}, and C = {e,f,g, h} . a.) (6 pts.) LIST the elements in sets A U B, B n C, and Ac . b.) (4 pts.) Determine the probabilities P(A) and P(B) . c.) (4 pts.) Determine the probabilities P(A n C') and P(A U C) . 2.) (9 pts) Assume the probability that a newborn is a boy is exactly 1 / 2 and the prob
ability it’s a girl is exactly 1 / 2. If gender outcomes from child to child are independent,
what is the probability that a family of 6 children will consist a.) of all girls ?
b.) of 4 boys and 2 girls ? c.) at least 1 girl ? 3.) (8 pts) A group of 15 people includes 8 men and 7 women. What is the probability
that a committee of 6 people chosen randomly will have exactly 4 women and 2 men? 4.) (12 pts) (Genetics~ Mendel’s First Law) Gregor Mendel (Austria 1856) studied pea
plants and the color of their ﬂowers determined by two genes in their chromosomes. Assume
that the following genotypes are possible : CC, Cc (same as CC), and cc, where types CC
and Cc produce RED ﬂowers and type cc produces WHITE ﬂowers. Suppose that you
have a batch of red and whiteﬂowering pea plants, where all three genotypes CC, Cc,
and cc are represented. Assume that 25% of the plants are type CC, 35% of the plants are
type Cc, and 40% of the plants are type cc. You will pick 1 parent plant at random from
the batch and cross it with a pea plant of genotype cc. What is the probability that the
offspring will have RED flowers ? l 5.) (12 pts.) Play the following game with your roommate. You roll a fair sixsided die
one time. If you roll a 1 or 5 you win 75 cents from your roommate. Otherwise you lose
30 cents to your roommate. What is your expected monetary outcome ? 6.) (12 pts.) A blood test for the HIV virus shows a positive (+) result in 95% of all cases
when the virus is actually present in an individual and in 8% of all cases when the virus is
NOT present in an individual (false positive). Assume that 15 out of every 100 people are
carriers of the virus. If a person tests positive (+) for HIV, what is the probability that
this person IS a carrier of the HIV virus ? 7.) (12 pts.) Consider a bag with 10 red and 15 white baseballs. Randomly select 1 ball. REPLACE it. Do this 20 times. Let random variable X be the number of red balls
selected. a.) What is P(X = 6) ? b.) Determine the expected value p = E (X ) . c.) Determine the standard deviation of X . 8.) (9 pts.) Toss a fair sixsided die twice. Let A be the event that the 1st toss is an even
number. Let B be the event that the sum of the two tosses is 7. Determine if A and B are
independent events. 9.) (12 pts.) Consider a sample space (2 of people made up of 400 men and 600
women. Deﬁne discrete random variables X : Q ———+ R and Y : Q ——+ R by t __ 0, if x is male (M)
X“) '— { 1, if as is female (F) and
0, if y sleeps less than 6 hours each night (NS) 1, if y sleeps 6 or more hours each night (S) my) = { The frequency of results are represented in the following table of values. Convert this
information into a joint probability table. (M) (F) (M) (F)
X20 x31 Xzo x_( What is the probability that a person selected at random is a.) a female ? b.) a male who sleeps less than 6 hours each night ? c.) a female or sleeps 6 or more hours each night ? The following EXTRA CREDIT PROBLEM is worth 10 points. This problem is OP
TIONAL. 1.) Assume there are 365 days in a year. In a group of 25 people, what is the probability
that at least two people have the same birthday (same month and day) ? ...
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 Spring '09
 Kouba
 Calculus

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