The answer depends on whether the children are picked at random. If they were selected from inside a girls' school the probability should be quite close to 0. Likewise, if the children were picked inside a boys' school.
If six children are picked at random from a large group of children with an equal number of boys and girls, then the answer is
6C2*(1/2)6 = 15/32 = 0.47, approx.
In a family with four children, the probability of having four boys is 1 in 16.
1/8
4/16 or 0.2 or 25%
50/50
50%
In a family with four children, the probability of having four boys is 1 in 16.
6 out of 9.
1/8
4/16 or 0.2 or 25%
50/50
Assuming that having boys and girls are equally likely, then the probability is 1/8. * * * * * You also need to assume that the children's genders are independent. They are NOT and depend on the parents' ages and genes.
Since the probability of having a son is about 1/2, the probability of the first 4 children being boys is about (1/2)4.
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, the probability of 13 boys in a family with 13 children is approx 0.00019.
The probability of having a boy or a girl is always 50/50 each time, regardless of previous outcomes. So the theoretical probability of having a girl after having three boys in a row is still 50%.
This is a Binomial Probability; p=0.5, n=10 & x=7. Since you want the probability of exactly 7, in the related link calculator, after placing in the above values, P(x=7) = 0.1172 or 11.72%.
25