Boy Or Girl??

The following problem is taken from Bazerman and Moore (2009) Judgement in Managerial Decision Making:

You and your spouse have had three children together, all of them girls. Now that you are expecting your fourth child, you wonder whether the odds favour having a boy this time. What is the best estimate of your probability of having another girl?

6.25% (1 in 16), because the odds of getting four girls in a row is 1 out of 16

50% (1 in 2), because there is roughly an equal chance of getting each gender

A percentage that falls somewhere between the two estimates (6.25-50 percent)

The answer is 50%. (The sperm that determines gender of the child does not know the gender of previous children! In other words, the gender of each child is independent of that their siblings.)

So what explains our potentially wayward intuition here?

According to Kahneman and Tversky (1974) "Chance is commonly viewed as a self-correcting process in which a deviation in one direction induces a deviation in the opposite direction to restore the equilibrium. In fact, deviations are not corrected as a chance process unfolds, they are merely diluted."

So there you go, hope this helps when you're expecting your fourth child...