I'm following the paper available here. The Binomial distribution is used to calculate the probability of obtaining 26 babies of the same sex from a total of 44 births. If the probability of giving birth to a boy is equal to that of a girl then - according to the paper -
The probability of observing at least 26 babies of the same sex in 44 births is 0.2912 under this assumption.
However if I calculate the probability of
x > 25 using the
pbinom() function in R as
> pbinom(25, 44, 0.5, lower.tail = FALSE)  0.146
I realize that
0.146 + 0.146 = 0.291, which could be taken to mean that the probability of getting 26 babies of the same sex =
P(x > 25) boys + P(x > 25) girls. Is this reasoning correct? If yes, then when I change x to be
x = 21 then
P(x > 21) = 0.56, in which case "probability of observing at least 22 children of the same sex would be
1.12 which seems wrong as the probabilities should be less than 1. What am I doing wrong?