Triolach4 Take home project.

This project must be done without any help from others so you must certify that you solved all problems without involving any third party ______(Your signature here)

You can use your calculator, it is not a “Third party”

2ptseachquestionorsub-questionwith all the work demonstrated on this paper.

Please submit your project online. You can print it out, have the work done, than take a shot, and send me a picture.

Showallthe workon this paperoron the paper attached and submitted to get points.

Your name ______

Inproblems1),2)and3)findindicatedprobabilities.

  1. Thetwo fairdicewith6sidesare rolled.WRITE A SAMPLE SPACE FOR AN EVENT:

Thesumoffaceupnumbers5.

1.______

  1. Whatisthe probability thatthesumofdaceupnumbers5? 2. ______
  1. Abagcontains2redmarbles,3bluemarbles,and 7greenmarbles.Onemarbleisrandomlyselected fromthebag.Findthefollowingprobabilities: (box your answer)

3a) Itwasnotabluemarble.3a.______

3b) Itwasredorbluemarble.

3b.______

  1. TheprobabilitythatLuiswillpasshisstatisticstestis 0.90, and the probability that Luis will pass his ESL test 0.95.

4a) Findtheprobabilitythathewillfailhisstatisticstest. 4a.______

4b) FindtheprobabilitythatLuis will pass at least one test.

4b.______

  1. a)Listthesamplespace:

Afamilyhastwochildren;recordthegendersinorderofbirth.

SAMPLE SPACE S =

b)Findtheprobabilitythatrandomlyselectedfamilyhasatleastonegirl

if P(G)=P(B) = 0.5 5b.______

Findtheindicatedprobability.

  1. Amanufacturingprocesshasa70%yield,meaningthat70%oftheproductsareacceptableand30%aredefective.Ifthreeoftheproductsarerandomlyselected findtheprobabilitythatallofthemareacceptable.

Findtheindicatedprobability.Give your answer as a fraction or a decimal rounded to

thenearestthousandth.

  1. Asampleof2differentcalculators(withoutreplacement)israndomlyselectedfrom agroup containing6that aredefectiveand24withoutdefects. ( 30 total)

Draw ATree diagram with probabilities assigned.

7a. Whatistheprobabilitythat bothcalculatorsaregood. (Use a tree diagram to find the indicated probability).

7a______

7b. Find the probability that the first calculator was good given the condition that the first one was defective!

7b.______

  1. Injuries and Motorcycle Helmet Color. A retrospective study was conducted to investigate a relationship between the colors of helmets worn by motorcycle driver and whether they are injured or killed in the crash. Results are given in the table below.

Black / White / Yellow/Orange / Red / Blue / Total
Not injured / 491 / 377 / 31 / 170 / 55 / 1124
Injured or killed / 213 / 112 / 8 / 70 / 26 / 429
Total / 704 / 289 / 39 / 240 / 81 / 1553

Find the following probabilities. Answer in two forms: as a not simplified fraction and decimal rounded to two decimal places.

a)P(Black AND Not Injured)a.______

b)P(Yellow/Orange OR Not Injured)b.______

c)P (Driver was Injured given the driver was inBlack helmet) c.______

d)P (Driver was Injured given the driver was inYellow/Orange helmet)

d.______

e)Compare results of c) and d), and explain in words why these probabilities are different, and what color you think is more safe for a motorcycle driver?

e.______

f)Support your answer in e) by determining whether event: “The Driver Was Injured or Killed” and “The Driver wore Yellow/Orange helmet” independent?

f.______

9. A polygraph test (PT).

Did the subject actually lie?

No (event C)Yes (event D) Total

Positive test result ( A ) 154257

PT indicated

that he subject lied

Negative test result (B) 32 941

PT indicated

that he subject did not ied

Total475198

1 of 98 test results is randomly selected. Describe in words the following events occurred:

A

9a ______

9b. Find the probability that the polygraph test was wrong. ______

9c. Find ODDS in FAVOR an event “ The test was wrong” , and comment on what these odds mean in the context of a story like if you are a Jury, and have to make a verdict Guilty/ Not Guilty.

9c.______

  1. A survey revealed that 50% of people are entertained by reading books, 34% are entertained by watching TV, and 16% are entertained by both books and TV.

10 a. Draw Venn Diagram.

10b .What is the probability that a person will be entertained by either books or TV?

10b.______

10c. What is the probability that a person will be entertained by TV only?

10c______

10d. What percent of people are entertained by neither books nor TV?

10d.______