GATE CSE
First time here? Checkout the FAQ!
x
+1 vote
96 views

1) A total of 46% of the voters in a certain city classify themselves as Independents, where as 30% classify themselves as Liberals and 24% say they are Conservatives. In s recent local election, 35% of the Independents, 62% of the Liberals and 58% of the Conservatives voted. A voter is chosen at random. Given that this person voted in the local election, the probability that he or she is an Independent is _________ ans  0.331

2) A family has children with probability P_i where P1=0.01,P2=0.25,P3=0.35,P4=0.3. A child from this family is randomly chosen. Given that this child is the eldest child in the family, the conditional probability that the family has 4 children _______.ans  0.18

 

asked in Probability by Active (2.1k points)   | 96 views

1 Answer

+1 vote
Best answer

Answer to 1st question :

Given , 

P(Independent)   =  0.46   =   r (say)

P(Liberal)   =   0.30       =    s

P(Conservative)   =  0.24   =  t

P(Vote | Independent)  =  0.35   =   u

P(Vote | Liberal)   =  0.62         =   v

P(Vote | Conservative)  =  0.58   =  w

So 

P(Independent | Vote)  =   ru / ( ru + sv + tw )

                                 =   (0.46 * 0.35) / [(0.46 * 0.35) + (0.3 * 0.62) + (0.24 * 0.58)]

                                 =    0.331

Hence the answer to the first question is 0.331

 

The second question has a bit lengthy calculation actually..

answered by Veteran (66.5k points)  
selected by

II)P1=0.01,P2=0.25,P3=0.35,P4=0.3.

P(E|P1)=1,P(E|P2)=0.5 , P(E|P3)=0.33,P(E|P4)=0.25.

$P(P4|E) = \frac{P(E|P4) * P(P4))}{ P(E|P3) * P(P3) +P(E|P2) * P(P2)+P(E|P1) * P(P1)+P(E|P4) * P(P4)}$

= 0.075 / 0.3255= 0.230

please explain the 2nd Q ..i have difficulty in understanding the Questn
P1 =>family has 1 child,P2=>family has 2 child same for P3,P4

P(E|P1) = eldest from family P1 = 1 ( only one child no comparision)

P(E|P2) = eldest from family P2 = 0.5 (  two child ,one is eldest and other young )

P(E|P3) = eldest from family P3 = 0.33 (  three child ,one is eldest and two  young )

P(E|P4) = eldest from family P4  = 0.25 (  four child ,one is eldest and three young )

Related questions



Top Users Jun 2017
  1. Bikram

    3704 Points

  2. Arnab Bhadra

    1502 Points

  3. Hemant Parihar

    1502 Points

  4. Niraj Singh 2

    1481 Points

  5. junaid ahmad

    1432 Points

  6. Debashish Deka

    1384 Points

  7. Rupendra Choudhary

    1220 Points

  8. rahul sharma 5

    1220 Points

  9. Arjun

    1158 Points

  10. srestha

    1006 Points

Monthly Topper: Rs. 500 gift card
Top Users 2017 Jun 26 - Jul 02
  1. Arjun

    198 Points

  2. akankshadewangan24

    152 Points

  3. Debashish Deka

    138 Points

  4. Hira Thakur

    130 Points

  5. Soumya29

    104 Points


23,399 questions
30,111 answers
67,489 comments
28,424 users