Acuitus Interview Question: A rustic village contains one... |

Interview Question

Senior Java Developer Interview Palo Alto, CA (US)

A rustic village contains one million married couples and

  no children. Each couple has exactly one child per year. Each couple wants a girl, but also wants to minimize the number of children they have, so they will continue to have children until they have their first girl. Assume that children are equally likely to be born male or female. Let p(t) be the percentage of children that are female at the end of year t. What is p(t)? "Can't tell" is a potential answer if you don't have sufficient information.

Interview Answer

6 Answers


can't tell

Interview Candidate on 05-Apr-2010

The answer is 2^-t

kamal kanna on 04-Mar-2014


kamal kanna on 04-Mar-2014

p(t) = 50% at all years (with some rounding)
P(1) = 1,000,000 children, 500,000 of them girls, 500,000 of them boys
P(2) = 500,000 more children (only those who had boys have another child), 250,000 girls, 250,000 boys
so overall, there are now 750,000 girls, and 750,000 boys
P(3) = 250,000 more children, 125,000 girls, 125,000 boys
so there are now 875,000 girls (with 500,000 being only children, 250,000 having one brother, and 125,000 having 2 brothers), and 875,000 boys
So, except for some rounding when the previous year's number of all boy families is an odd number, you will always have 50% of each

Rachel on 03-Jun-2015

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