Boy or Girl Paradox Calculator

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The classic variant yields 1/3; knowing the older child is a boy gives 1/2; specifying a rare attribute (day of birth) shifts the answer toward 1/2.
The baseline probability that any single child is a boy. Default 0.5 (50/50 sex ratio).
(0-1)
P(both boys)Near 1/3 (exhaustive)
0.3333%

Probability that both children are boys given the stated information

P(not both boys)0.6667%
Exact fraction (approx)1/3
Effective sample space size3
Favourable outcomes (both boys)1
P(both boys)0.3333%
P(other is a girl)0.6667%

Given at least one boy, both being boys has probability 1/3 (33.33%).

  • The sample space shrinks from 4 outcomes to 3 (BB, BG, GB) once GG is excluded, leaving BB as 1 of 3.
  • This 1/3 answer assumes someone surveyed the whole family and reported "at least one boy".
  • If instead you randomly met one child and they happened to be a boy, the correct answer becomes 1/2.

Next stepThe paradox is resolved by asking: how was the information obtained? Random sampling of one child gives 1/2; surveying both children gives 1/3.

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