Respuesta :
Answer:
The second pair of grandparents have approximately 12 to 19 boys as grandchildren.
Explanation:
The probability of a grandchild being a girl or a boy is same, i.e., [tex]\frac{1}{2}[/tex].
The first pair of grandparents have 4 grandchildren.
The second pair of grandparents have 32 grandchildren.
If first pair of grandparents have between 40% to 60% boys as grandchildren then the number of boys are in the limit,
[tex](40\%\ of 4,\ 60\%\ of 4)=(1.6, 2.4)\approx(2, 3)[/tex]
Thus, the first pair of grandparents have approximately 2 to 3 boys as grandchildren.
If second pair of grandparents have between 40% to 60% boys as grandchildren then the number of boys are in the limit,
[tex](40\%\ of 32,\ 60\%\ of 32)=(12.8, 19.2)\approx(13, 19)[/tex]
Thus, the second pair of grandparents have approximately 12 to 19 boys as grandchildren.
So, it is clear that the second pair of grandparents are more likely to have between 40% and 60% boys as grandchildren.
Also according to the law of large numbers as the sample size increases the probability of an event gets closer to the theoretical probability.
