# DSE 2012- Question 42-44, 48 and 55-56. Classic List Threaded 23 messages 12
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## DSE 2012- Question 42-44, 48 and 55-56.

 Ok, so a lot of confusion regarding how to go about all of these questions. Question 55-56 would require some context so I'll paste the link as well as the questions. QUESTION 42. A fair coin is tossed until a head comes up for the 1st time. The probability of this happening on an odd-numbered toss is (a) 1/2 (b) 1/3 (c) 2/3 (d) 3/4 Answer: (c) QUESTION 43. An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, then the number of outcomes B must have so that A and B are independent, is (a) 4 (b) 3 or 9 (c) 6 (d) 5 or 10 Answer: (d) QUESTION 44. Consider the system of equations x + y = 0 x + y = 0 ; ;  and  are i.i.d random variable. Each of them takes value 1 and 0 with equal probability. Statement A: The probability that the system of equations has a unique solution is 3/8. Statement B: The probability that the system of equations has at least one solution is 1. (a) Both the statements are correct (b) Both the statements are false (c) Statement A is correct but B is false (d) Statement B is correct but A is false Q 48. A rectangle has its lower left hand corner at the origin and its upper right hand corner on the graph of f(x) = x^2 + (1/x^2). For which x is the area of the rectangle minimized? (a) x= 0 (b) x = Infinity (c) x = (1/3)^1/4 (d) x = 2^1/3 For 55 and 56: http://economicsentrance.weebly.com/uploads/1/1/0/5/1105777/2012-option-a.pdf
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 48) we have to minimize d area of d rectangle area= xy =x(x^2 +1/x^2) . now minimise it .
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 In reply to this post by Darth Vader q42)  P(H)=P(T)=1/2 so prob of getting head in odd numbered toss wud be p(H)+p(TTH)+p(TTTTH)+p(TTTTTTH)...so on = 1/2 +1/2*1/2*1/2 + 1/2*1/2*1/2*1/2*1/2..so on...  its a infinite gp with a=1/2 and r=(1/2)^2 sum of infinte  gp= a/(1-r)= (1/2)/(1-(1/2)^2)= 2/3
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 In reply to this post by Darth Vader .44)    ax+by=0         Cx+dy =0                 P(0)=P(1)=1/2       we can check the consistency of the above eqn using AX=0       |A|=ad-bc eqn (1)                a,b,c,d are iid rv        we will create the sample space and find the joint prob        a    d      P(A).P(d)        0    1        1/4        1    0        1/4        0    1        1/4        1    1        1/4                b    c      P(b).P(c)        0    1        1/4        1    0        1/4        0    1        1/4        1    1        1/4       from eqn 1 if system of eqn has unique soln ad-bc is nt equal to zero      case 1 a=0,d=1 gives ad=0...b=1=c gives bc=1  ad-bc nt equal to zero             so P=1/4.1/4=1/16      case 2 and 3, when a=1,0 and d= 0,1  resp..ad=0 and b=c=1 gives bc=1...              p=1/4.1/4+1/4.1/4=2/16      case 4,5,6    when a=1,d=1..ad=1   b=0,1,0 and c=1,0,1 resp giving bc=0                    p=1/4.1/4 + 1/4.1/4 +1/4.1/4= 3/16              adding all the six cases which gives the probability of a unique soln =6/16 =3/8
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 Thanks! Any idea about q 55-56?
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 In reply to this post by wolverine Also how do we show that there's certainty of a solution?
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 In reply to this post by maahi Thanks! Any idea about q55-56?
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 Q 55) Let x represent mark up F(u,A)= (A/u) - 1 F(u,A) = 1/(1+x) A/u -1 = 1/(1+x) Re arranging the above equation, u = A(1+x)/(2+x)-----(1) Hence, this is the answer to q 55. For Q 56) Use equation 1, and Simply substitute the variables with any number, you will get the answer. I put: x=1 A=90 Y(gamma)= 10% So if you put these numbers in eq 1, you get: 2/3(90)=60 Now if you increase A by Y, i.e., 90 by 10%, the corresponding increase in u, i.e. 60, is also 10%, i.e. Y. So if the workers productivity increases at a constant rate Y, then the rate of unemployment also increases by Y. Hence answer is (a)
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 Hi Ankita, In 56, how can you say "u" also increases by "gamma"? Shouldn't it be a fraction of "gamma"?
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 QUESTION 43. An experiment has 10 equally likely outcomes. Let A and B be two non-empty events of the experiment. If A consists of 4 outcomes, then the number of outcomes B must have so that A and B are independent, is (a) 4 (b) 3 or 9 (c) 6 (d) 5 or 10 pls Help
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## Re: DSE 2012- Question 42-44, 48 and 55-56. M.A Economics Delhi School of Economics 2013-15 Email Id:sumit.sharmagi@gmail.com
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 y shud x be <=4 ?
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 bcoz intersection btw two events means probability of happening of both the events simultaneously...so x should be <= 4 bcoz p(A)=4...( In other words, maximum elements that  could be common btw A & B will be less than or equal to 4..) M.A Economics Delhi School of Economics 2013-15 Email Id:sumit.sharmagi@gmail.com
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 can u xplain d part where you chose x=2 nd 4 n rejected  1 ? i m nt able to read d picture clearly
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 In reply to this post by Ayushya Kaul No it does not increase by a 'fraction' of gamma. Try using numbers in place of variables. It makes your work a whole lot easier. P.S. My name is not Ankita. It's Ankit:-P
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 In reply to this post by maahi @Maahi: we reject 1 n 3 bcoz outcomes are always in the integer form. suppose if we take x=1 the P(B)=2.5/10 which can't be possible bcoz outcome can take only integer values from 1 to 10 only...not 2.5 which means 2 n a half outcome. M.A Economics Delhi School of Economics 2013-15 Email Id:sumit.sharmagi@gmail.com
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 ok thanks a lot :-)
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 In reply to this post by Ankit Agrawal Ok, great. Ha, apologies for the mistake. Cheers!
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## Re: DSE 2012- Question 42-44, 48 and 55-56.

 In reply to this post by wolverine could you plz tell me abt Q 40. My logic is as follows but doesnt quite satisfy. P(Green)=P(Red)= 0.5  as the balls are placed back each time is it that we would expect to lose as much money by drawing a red ball, as much we earn by picking a green ball; as the prob of doing the two are the same?? and rs 10-10=0??