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The following table identifies a group of children by one of four hair colors, and by type of hair.

Hair Type Brown Blond Black Red Totals
Wavy 20 15 3 43
Straight 80 15 12
Totals 20 215
  • Complete the table above.
  • What is the probability that a randomly selected child will have wavy hair?
  • What is the probability that a randomly selected child will have either brown or blond hair?
  • What is the probability that a randomly selected child will have wavy brown hair?
  • What is the probability that a randomly selected child will have red hair, given that he has straight hair?
  • If B is the event of a child having brown hair, find the probability of the complement of B.
  • In words, what does the complement of B represent?
  • 43 215
  • 120 215 size 12{ { { size 8{"120"} } over { size 8{"215"} } } } {}
  • 20 215
  • 12 172
  • 115 215 size 12{ { { size 8{"115"} } over { size 8{"215"} } } } {}

A previous year, the weights of the members of the San Francisco 49ers and the Dallas Cowboys were published in the San Jose Mercury News . The factual data are compiled into the following table.

Shirt# ≤ 210 211-250 251-290 290≤
1-33 21 5 0 0
34-66 6 18 7 4
66-99 6 12 22 5

For the following, suppose that you randomly select one player from the 49ers or Cowboys.

  • Find the probability that his shirt number is from 1 to 33.
  • Find the probability that he weighs at most 210 pounds.
  • Find the probability that his shirt number is from 1 to 33 AND he weighs at most 210 pounds.
  • Find the probability that his shirt number is from 1 to 33 OR he weighs at most 210 pounds.
  • Find the probability that his shirt number is from 1 to 33 GIVEN that he weighs at most 210 pounds.
  • If having a shirt number from 1 to 33 and weighing at most 210 pounds were independent events, then what should be true about P(Shirt# 1-33 | ≤ 210 pounds) ?

Approximately 281,000,000 people over age 5 live in the United States. Of these people, 55,000,000 speak a language other than English at home. Of those who speak another language at home, 62.3% speak Spanish. ( Source: http://www.census.gov/hhes/socdemo/language/data/acs/ACS-12.pdf )

Let: E = speak English at home; E' = speak another language at home; S = speak Spanish;

Finish each probability statement by matching the correct answer.

Probability Statements Answers
a. P(E') = i. 0.8043
b. P(E) = ii. 0.623
c. P(S and E') = iii. 0.1957
d. P(S|E') = iv. 0.1219

  • iii
  • i
  • iv
  • ii

The probability that a male develops some form of cancer in his lifetime is 0.4567 (Source: American Cancer Society). The probability that a male has at least one false positive test result (meaning the test comes back for cancer when the man does not have it) is 0.51 (Source: USA Today). Some of the questions below do not have enough information for you to answer them. Write “not enough information” for those answers.

Let: C = a man develops cancer in his lifetime; P = man has at least one false positive

  • Construct a tree diagram of the situation.
  • P(C) =
  • P (P|C) =
  • P (P|C' ) =
  • If a test comes up positive, based upon numerical values, can you assume that man has cancer? Justify numerically and explain why or why not.

In 1994, the U.S. government held a lottery to issue 55,000 Green Cards (permits for non-citizens to work legally in the U.S.). Renate Deutsch, from Germany, was one of approximately 6.5 million people who entered this lottery. Let G = won Green Card .

  • What was Renate’s chance of winning a Green Card? Write your answer as a probability statement.
  • In the summer of 1994, Renate received a letter stating she was one of 110,000 finalists chosen. Once the finalists were chosen, assuming that each finalist had an equal chance to win, what was Renate’s chance of winning a Green Card? Let F = was a finalist . Write your answer as a conditional probability statement.
  • Are G and F independent or dependent events? Justify your answer numerically and also explain why.
  • Are G and F mutually exclusive events? Justify your answer numerically and also explain why.
P.S. Amazingly, on 2/1/95, Renate learned that she would receive her Green Card -- true story!

  • P ( G ) = 0 . 008 size 12{P \( G \) =0 "." "008"} {}
  • 0.5
  • dependent
  • No

Questions & Answers

can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
im not good at math so would this help me
Rachael Reply
yes
Asali
I'm not good at math so would you help me
Samantha
what is the problem that i will help you to self with?
Asali
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Collaborative statistics (custom lecture version modified by t. short). OpenStax CNX. Jul 15, 2013 Download for free at http://cnx.org/content/col11543/1.1
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