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Estimating the Weight of a 747 and Gender Ratio in Boy-Preference Countries

This document discusses two distinct problems often posed in interviews. The first problem involves estimating the weight of a Boeing 747 by comparing it to buses, arriving at an approximate weight of 43 tons. The second problem explores a scenario in a country where couples continue having children until they have a boy, raising the question of the boy-to-girl ratio under this strategy. Through logical reasoning and examination of possible outcomes, it concludes that the expected ratio of boys to girls is 1:1.

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Estimating the Weight of a 747 and Gender Ratio in Boy-Preference Countries

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  1. Google/Microsoft interview

  2. Problem 1 • Estimate the weight of a 747.

  3. Problem 1 • Estimate the weight of a 747. • Ok, 747 is a vehicle designed to carry people. We don’t know much about planes, but let’s think by proxy. What other large vehicles carry passengers? • Busses. Assume 747 = 6 buses. 4 in a row + 2 on top. Each bus ~ 60 people. So 747 ~ 360 people. Sounds about right. A bus weighs 5-10 tons. So, a 747 weighs between 6*5 and 6*10 = 30-60 tons. (43 tons, actually).

  4. Problem 2 • In a country where couples want boys, they use the following strategy: couples have children until they have a boy, then stop. What is the ratio of boys to girls in this country?

  5. Problem 2 • In a country where couples want boys, they use the following strategy: couples have children until they have a boy, then stop. What is the ratio of boys to girls in this country? • 1St step: get your feet wet. Play with the problem. Start with N=2 couples. You can have 2 boys. Or you can have 4 girls and then 2 boys. So, looks like all possible ratios are possible.

  6. Problem 2 • In a country where couples want boys, they use the following strategy: couples have children until they have a boy, then stop. What is the ratio of boys to girls in this country? • 1St step: get your feet wet. Play with the problem. Start with N=2 couples. You can have 2 boys. Or you can have 4 girls and then 2 boys. So, looks like all possible ratios are possible. • Of course, each of these outcomes has its own different probability. So, we could consider all outcomes and work out the probabilities. But that would be kind of difficult…

  7. Problem 2 • In a country where couples want boys, they use the following strategy: couples have children until they have a boy, then stop. What is the ratio of boys to girls in this country? • Alternative. Let’s go to the large N limit. Appropriate for “country”. Will simplify things. Exactly ½ couples will have boys, ½ will have girls. • First, what is easier to find, NB or NG? Of course, NB = N. So, need to focus on NG • Draw a BIG diagram.

  8. Problem 2 Count girls: NG = N/2 + N/4 + N/8 + … = N = NB Offspring generation # 3 N/8 BBB GGG 2 BBBBBB GGGGGG N/4 BBBBBBBBBBBBB GGGGGGGGGGGGG N/2 1 N/2 couples

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