Probability questions please anwer all 4 questions not just one 1. 2. 3. 4. In a

Question

Probability questions please anwer all 4 questions not just one

1.

2.

3.

4.

In an attitudinal survey on strict gun-control legislation administered to 800 U.S. adults, the following results were obtained: n favor Against Shot a gun 75 200 Never shot a gun 425 100 If one of the 800 adults is chosen at random, determine each of the following probabilities: Round all answers to three decimal places. 1st choice 0.625 2nd choice 0.250 3rd choice 0.469 4th choice 0.190 P(shot a gun or against)- P(shot a gun and against) P(against never shot a gun)- P(in favor)

Explanation / Answer

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1. 800 total US adults.
P(shot a gun or against) =(75+200+100+200)-200 / 800 = 375/800=.4688 or .469

P(shot a gun and against) = 200/800 = .25
There are 250 people who shot and gun and against

P(against|never shot a gun) = 100/(100+425) = .1905 or .190
P(in favor) = 75+425 / 800 =500/800 = 0.625

2. P(3 tails) = (1/2)^3 = 1/8 = .125
P(at least 1 head) = 1-P(no head) = 1-P(all tails) = 1-(1/2)^3 = .875
P(Exactly 1 head) = 3C1 ( 1/2)*(1/2)^2 = .375

3.P( 2nd is red|1st is green) = 10/(10+14) = 10/24 = .417

4. P(he will be absent 10 or more days |he'smoker) = Smoker and 10 or more / smoker
= 78/(78+34)
= .696

Events are independent if they satisfy the below condition:

P(a and b) = P(a)*P(b)
therefore,
Also, P(being absent for 10 or more) = (78+28)/400 = .2650
P(smoker) = (78+34)/400 =.28
P(being absent for 10 or more)*P(smoker) =.265*.28= .0742....1
P(smoker and absent for 10 or more) = 78/400 = .195..........2

1 and 2 aren't equal and hence these events are not indepedent

Choice D is correct, as smoking and abscence are not independent and answer to the 1st Qn is .696

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