A primitive village follows a strange custom. They have babies only to have a boy. Whenever a boy is born in a family, they stop having babies and whenever a girl is born, they have a baby again and again till a boy is born.
The probability of having a boy is same as the probability of having a girl. What will be the proportion of boys to girls in the village after some time?
Choose the correct answer:  A) 2.1  B) 1.3  C) 5.1  D) 2.3  E) 1.1
E   1:1 (approx)   Explanation:   We know that the probability of having a boy or having a girl is same and thus, half of the couples will stop after having a boy child. Half of the others will have a girl and will have a baby again. Out of those half of the couples, half will have a boy and will stop and half will have a girl again. This will keep on going like this.   Now, if there are X number of couples, there will be X boys.   1/2 have a boy and stop: 0 girls   1/4 have a girl, then a boy: X/4 girls   1/8 have 2 girls, then a boy: 2*X/8 girls   1/16 have 3 girls, then a boy: 3*X/16 girls   1/32 have 4 girls, then a boy: 4*X/32 girls   …   Total: X boys and   1X 2X 3X 4X   – + – + – + — +… = ~X   Therefore, the proportion of boys to girls will be extremely close to 1:1
<result>E</result>
A primitive village follows a strange custom. They have babies only to have a boy. Whenever a boy is born in a family, they stop having babies and whenever a girl is born, they have a baby again and again till a boy is born.
The probability of having a boy is same as the probability of having a girl. What will be the proportion of boys to girls in the village after some time?