Probability Question for Sec 4

• 787180

  21 Feb 09, 14:47

  Suppose that 45% and 40% of Singaporeans approve and diapprove the idea of building a casino respectively.If three Singaporeans are interviewed at random,find the prob that a)all of them will either approve or disapprove of the idea b)at least two of them will not approve of the idea c) at most one of them will approve of the idea. Let A=approve.DA=disapprove,N=neither approve nor disapprove p(A)= 0.45,P(DA)=0.40,P(N)=1-0.45-0.40=0.15 a) P(all approve or disapprove)=P(AAA)+P(DA.DA.DA) =0.45x0.45x0.45+0.40x0.40x0.40 =)0.155125 but correct answer is 4913/8000 b) P(at least 2 of them will not approve)=P(DA.DA.A)+P(DA.DA.DA)+P(DA.DA.N)=0.40x0.40x0.45+0.40x0.40x0.40+0.40x0.40x0.15 =0.16 but correct answer is 44/125 c)P(at most one of them will approve)=P(A.DA.DA)+P(A.DA.N)+P(A.N.DA)+P(DA.DA.DA)+P(N.N.N)=0.45x0.40x0.40+0.45x0.40x0.15+0.45x0.15x0.40+0.40x0.40x0.40+0.15x0.15x0.15=0.193375 but correct answer is 2299/4000. Can someone plse advise..thanks in advance
• charlize

  21 Feb 09, 14:51

  Calculate all you want.  The casino will still be built.

   

  But I digress.

• 787180

  21 Feb 09, 14:55

  helping a niece with her sch hwork but lost touch after so many years,hence see whether any guru on maths can help..no time for digression
• TenSaru

  21 Feb 09, 16:06

  (a) P(all of them have opinion) = 0.85 X 0.85 X 0.85 = 4913/8000
  
  (b) Let X = not disapprove; P(X)=0.6
         P(at least 2 disapprove) = P(DDX) + P(DXD) + P(XDD) + P(DDD)
                                                = 3 (0.4X0.4X0.6) + 0.4X0.4X0.4
                                                =44/125

  (c) Let NA = not approve; P(NA) = 1-0.45 = 0.55

      P(at most 1 approve) = P(all NA) + 3 P(A.NA.NA)

                                         = 0.55X0.55X0.55 + 3(0.45X0.55X0.55)

                                         = 2299/4000

   

• TenSaru

  21 Feb 09, 16:17

  Opps... In my working D= disapprove

• Mr.Teo

  21 Feb 09, 19:18

  amazing question.

• candiz

  21 Feb 09, 21:39

  Originally posted by 787180:

  Suppose that 45% and 40% of Singaporeans approve and diapprove the idea of building a casino respectively.If three Singaporeans are interviewed at random,find the prob that
  a)all of them will either approve or disapprove of the idea

  b)at least two of them will not approve of the idea

  c) at most one of them will approve of the idea.

  Let A=approve.DA=disapprove,N=neither approve nor disapprove

  p(A)= 0.45,P(DA)=0.40,P(N)=1-0.45-0.40=0.15

  a) P(all approve or disapprove)=P(AAA)+P(DA.DA.DA)

  =0.45x0.45x0.45+0.40x0.40x0.40
                

  =)0.155125 but correct answer is 4913/8000
                

  b) P(at least 2 of them will not approve)=P(DA.DA.A)+P(DA.DA.DA)+P(DA.DA.N)=0.40×0.40×0.45+0.40×0.40×0.40+0.40×0.40×0.15
  =0.16 but correct answer is 44/125

  c)P(at most one of them will approve)=P(A.DA.DA)+P(A.DA.N)+P(A.N.DA)+P(DA.DA.DA)+P(N.N.N)=0.45×0.40×0.40+0.45×0.40×0.15+0.45×0.15×0.40+0.40×0.40×0.40+0.15×0.15×0.15=0.193375 but correct answer is 2299/4000.

  Can someone plse advise..thanks in advance

  stats is nightmare for me

• SBS261P

  22 Feb 09, 01:38

  haha...

  what TenSaru means is that you treat the 3 fellas as individuals. so the order in which they approve / disapprove matters.

  e.g. A, B approve, but C disapprove is 1 case.

  e.g. A, C approve, but B disapprove is another case.

  your original working didn't factor in this consideration... you must "permute" (so called) them, hence the multiplication by a factor of 3.

  otherwise your working is fine... =)

  hope this helps you understand TenSaru's working better.

• 787180

  22 Feb 09, 10:14

  Thanks Tensaru and SBS261P...but why is 1-0.45-0.40=0.15(ie neither approve nor disapprove not used in this question).Can enlighten when one add and when one multiply...wad independent and mutually exclusive..quite difficult to explain to my neice..thanks again all of U
• eagle

  22 Feb 09, 10:21

  Originally posted by 787180:

  Thanks Tensaru and SBS261P…but why is 1-0.45-0.40=0.15(ie neither approve nor disapprove not used in this question).Can enlighten when one add and when one multiply…wad independent and mutually exclusive..quite difficult to explain to my neice..thanks again all of U

  Add when it is an OR case (means either this or that)
  Multiply when it is an AND case (means must be this and that together)

  Question didn't really ask for neutral cases, so no need to use the 0.15 lor...

   

   

  P.S. happily adding question to examworld

• 787180

  22 Feb 09, 22:46

  Questions for Tensaru...from his earlier calculations below. b) Let X = not disapprove; P(X)=0.6 P(at least 2 disapprove) = P(DDX) + P(DXD) + P(XDD) + P(DDD) = 3 (0.4X0.4X0.6) + 0.4X0.4X0.4 =44/125 (c) Let NA = not approve; P(NA) = 1-0.45 = 0.55 P(at most 1 approve) = P(all NA) + 3 P(A.NA.NA) = 0.55X0.55X0.55 + 3(0.45X0.55X0.55) = 2299/4000 b) will not approve means disapprove why U don't take 0.40 as given from the start why U take the complement 1-0.40 ? c) Not approve isn't that =disapprove i.e 0.40 why take the complement 1-0.45(approve,given at start of question)...confused leh
• dlocenot

  23 Feb 09, 17:53

  This question is very poorly designed.

• TenSaru

  24 Feb 09, 21:01

  b) Not Disapprove = approve(0.45) + no opinion(0.15) = 1 - Disapprove

  If someone doesn't disapprove doesn't mean he approves; he may belong to the 3rd category of people with no opinion (neutral)

  c) Same here for c,

  Not Approve = Disapprove(0.40) + no opinion(0.15)

  Since the singaporeans are picked at random, there is still a chance that 1 (or more) singaporean has no opinion, so the neutral cases(0.15) has to be considered

   

• SBS261P

  25 Feb 09, 02:59

  it's the same idea as:

  "she's not fat"

  but doesn't mean she's slim... she can be in-between.... =D