Our twelve-year-old daughter Meghna asked us over dinner a few days ago: "If you toss a coin seven times, and all tosses come up heads, what is the probability of the eighth toss also turning up head?" I decided to give her a proper scientific answer, explaining the process of Bayesian updating, in the spirit of "Letters From A Father To His Daughter," by Jawaharlal Nehru, the first prime minister of independent India, who wrote letters, on the history of India, from H.M. prisons (for participating in India's struggle for independence from foreign rule), to his then-young daughter, Indira Priyadarshini, who, as Indira Gandhi, went on to become India's most consequential prime minister in her own right. I show that the answer depends on how sure one is about the prior valuation of the probability that the coin is fair. I then extend the analysis to valuation of the probability of gender-neutrality of birth on the basis of the observed number of female and male births in the U.S. and India.
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