Consider two pairs of grandparents. The first pair has 4 grandchildren and the second pair has 32 grandchildren. Which of the two pairs is more likely to have between 40% and 60% boys as grandchildren, assuming that boys and girls are equally likely as children? Why?

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., .

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,

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,

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.