3 out of 7
If both tosses are fair, the probability of that outcome is one in four.
The conditional probability is 1/4.
Assuming it is a fair coin, the probability is 1/24 = 1/16.
The probability is 1/2.
The probably of four girls in a family with four children is 1/16. I got this answer because: Probability of a girl is 1/2 and to get all girls you would multiply it by 1/2 for the rest of the girls.
In a family with four children, the probability of having four boys is 1 in 16.
3 out of 7
50-50
In a world in which every family has seven children (quite unlikely!) the probability would be 35/128 = 0.273. However in the world that we live in, families with 7 children are very rare and so the answer would be 0.273 of that very rare proportion.
1 in 2
If both tosses are fair, the probability of that outcome is one in four.
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 change occurred because the probability of having a boy is always 50/50 each time a child is born, regardless of the gender of previous children. Having four girls has no impact on the gender of the fifth child.
2/4
It is difficult to answer this question properly. One reason is that children's genders are not independent of one another: the gender depends on the parents' genetics and their age. The second reason is that the probability of a girl is not 0.50 but approx 0.48. However, if you ignore reality, then the answer is (1/2)4 = 1/16
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 girl is approx 0.48, the probability of 2 or more girls is 0.6617.