Within a certain city, exactly 50% of the population is women.

Consider the following two

scenarios:

a)

There will be fewer than 200 women in a 500 person simple random sample from this city .

b)

There will be fewer than 400 women in a 1000 person simple random sample from this city.

Which of these scenarios is more likely?

Or are they equally likely?

Why?

[Note: This problem should not require much computation].