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A community swim team has 150 members. Seventy-five of the members are advanced swimmers. Forty-seven of the members are intermediate swimmers. The remainder are novice swimmers. Forty of the advanced swimmers practice four times a week. Thirty of the intermediate swimmers practice four times a week. Ten of the novice swimmers practice four times a week. Suppose one member of the swim team is chosen randomly.

a. What is the probability that the member is a novice swimmer?

a. 28 150

b. What is the probability that the member practices four times a week?

b. 80 150

c. What is the probability that the member is an advanced swimmer and practices four times a week?

c. 40 150

d. What is the probability that a member is an advanced swimmer and an intermediate swimmer? Are being an advanced swimmer and an intermediate swimmer mutually exclusive? Why or why not?

d. P (advanced intermediate) = 0, so these are mutually exclusive events. A swimmer cannot be an advanced swimmer and an intermediate swimmer at the same time.

e. Are being a novice swimmer and practicing four times a week independent events? Why or why not?

e. No, these are not independent events.
P (novice practices four times per week) = 0.0667
P (novice) P (practices four times per week) = 0.0996
0.0667 ≠ 0.0996

Try it

A school has 200 seniors of whom 140 will be going to college next year. Forty will be going directly to work. The remainder are taking a gap year. Fifty of the seniors going to college play sports. Thirty of the seniors going directly to work play sports. Five of the seniors taking a gap year play sports. What is the probability that a senior is taking a gap year?

P = 200 140 40 200 = 20 200 = 0.1

Felicity attends Modesto JC in Modesto, CA. The probability that Felicity enrolls in a math class is 0.2 and the probability that she enrolls in a speech class is 0.65. The probability that she enrolls in a math class | that she enrolls in speech class is 0.25.

Let: M = math class, S = speech class, M | S = math given speech

  1. What is the probability that Felicity enrolls in math and speech?
    Find P ( M S ) = P ( M | S ) P ( S ).
  2. What is the probability that Felicity enrolls in math or speech classes?
    Find P ( M S ) = P ( M ) + P ( S ) - P ( M S ).
  3. Are M and S independent? Is P ( M | S ) = P ( M )?
  4. Are M and S mutually exclusive? Is P ( M S ) = 0?

a. 0.1625, b. 0.6875, c. No, d. No

Try it

A student goes to the library. Let events B = the student checks out a book and D = the student check out a DVD. Suppose that P ( B ) = 0.40, P ( D ) = 0.30 and P ( D | B ) = 0.5.

  1. Find P ( B D ).
  2. Find P ( B D ).
  1. P ( B D ) = P ( D | B ) P ( B ) = (0.5)(0.4) = 0.20.
  2. P ( B D ) = P ( B ) + P ( D ) − P ( B D ) = 0.40 + 0.30 − 0.20 = 0.50

Studies show that about one woman in seven (approximately 14.3%) who live to be 90 will develop breast cancer. Suppose that of those women who develop breast cancer, a test is negative 2% of the time. Also suppose that in the general population of women, the test for breast cancer is negative about 85% of the time. Let B = woman develops breast cancer and let N = tests negative. Suppose one woman is selected at random.

a. What is the probability that the woman develops breast cancer? What is the probability that woman tests negative?

a. P ( B ) = 0.143; P ( N ) = 0.85

b. Given that the woman has breast cancer, what is the probability that she tests negative?

b. P ( N | B ) = 0.02

c. What is the probability that the woman has breast cancer AND tests negative?

c. P ( B N ) = P ( B ) P ( N | B ) = (0.143)(0.02) = 0.0029

d. What is the probability that the woman has breast cancer or tests negative?

d. P ( B N ) = P ( B ) + P ( N ) - P ( B N ) = 0.143 + 0.85 - 0.0029 = 0.9901

e. Are having breast cancer and testing negative independent events?

e. No. P ( N ) = 0.85; P ( N | B ) = 0.02. So, P ( N | B ) does not equal P ( N ).

f. Are having breast cancer and testing negative mutually exclusive?

f. No. P ( B N ) = 0.0029. For B and N to be mutually exclusive, P ( B N ) must be zero.

Questions & Answers

Do somebody tell me a best nano engineering book for beginners?
s. Reply
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket 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
I'm interested in nanotube
Uday
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
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
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
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Introductory statistics. OpenStax CNX. Aug 09, 2016 Download for free at http://legacy.cnx.org/content/col11776/1.26
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