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41% of a certain​ country's voters think that it is too easy to vote in their country. You randomly select 12 likely voters. Find the probability that the number of likely voters who think that it is too easy to vote is​ (a) exactly​ three, (b) at least​ four, (c) less than eight.

Guest Apr 24, 2017
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 #1
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(b) atleast 4

Guest Apr 24, 2017
 #2
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We have a binomial probabilty here

 

Exactly three

 

C(12,4) (.41)^3 (.59)^9  ≈ 29.55%

 

At least 4  =

 

1 - C(12,0)(.59)^12 - C(12,1)(.41)(.59)^11 - C(12,2)(.41)^2(.59)^10 - C(12,3)(.41)^3(.59)^9  ≈ 79.5%

 

Less than 8  =

 

C(12,0)(.59)^12 + C(12,1)(.41)(.59)^11 + C(12,2)(.41)^2(.59)^10 + C(12,3)(.41)^3(.59)^9 +

C(12,4)(.41)^4(.59)^8 + C(12,5)(.41)^5(.59)^7 + C(12,6)(.41)^6(.59)^6 + C(12,7)(.41)^7(.59)^5 ≈ 93.38%

 

 

 

cool cool cool

CPhill  Apr 24, 2017

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