Suppose there were 4,065,014 births in a given year. Of those births, 2,081,287 were boys and 1,983,727 were girls.
a) If we randomly select two women from the population who then become pregnant, what is the probability both children will be boys?
b) If we randomly select two women from the population who then become pregnant, what is the probability that at least one child is a boy?
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a) The probability of selecting a boy for the first child is 2,081,287/4,065,014.
The probability of selecting a boy for the second child (given that the first child is also a boy) is (2,081,287-1)/(4,065,014-1).
Therefore, the probability of both children being boys is (2,081,287/4,065,014) * ((2,081,287-1)/(4,065,014-1)).
Calculating this, the probability of both children being boys is approximately 0.2583.
b) The probability of at least one child being a boy is the complement of the probability of both children being girls.
So, the probability of at least one child being a boy is 1 - (1,983,727/4,065,014) * ((1,983,727-1)/(4,065,014-1)).
Calculating this, the probability of at least one child being a boy is approximately 0.7417.
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