-- Zero if she has 0, 1, 2, or 3 children.
-- Roughly 1/16 = 6.25 percent if she has 4 children.
-- Roughly 5/32 = 15.6 percent if she has 5 children.
-- Roughly 15/64 = 23.4 percent if she has 6 children.
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In a family with four children, the probability of having four boys is 1 in 16.
50-50
There is no simple answer to the question because the children's genders are not independent events. They depend on the parents' ages and their genes. However, if you assume that they are independent events then, given that the probability of a boy is approx 0.52 in all cases, the overall probability is 0.0624.
The probability of rolling a four on an eight sided octahedron is 1 in 8, or 0.125.
The probability of having a boy or a girl is always 50/50 because the female has to X sex chromosomes and the male has one X and one Y sex chromosome. If you do a Punnet Square, there will be two squares with XY and two squares with XX. With four squares in all that makes a 50/50 chance.