Hospital Probability Question

[thegreenroad45]

I am in Year 10 and we are doing probability.

There are two hospitals in a certain town: a small one and a large one. In the small hospital, an average of 15 babies are born each day; in the large hospital, an average of 45 are born each day. Assume that the likelihood of giving birth to a boy is 50%.
In the small hospital, a record has been kept of the days (call them “small blue days”) during the year 2013 on which more than 9 boys were born. In the large hospital, a record has been kept of the days (“large blue days”) in 2013 on which more than 27 boys were born. How does the number of small blue days compare to the number of large blue days?

Proposition A: The expected number of small blue days is equal to the expected number of large blue days.

Proposition B: The expected number of small blue days is not equal to the expected number of large blue days.

 

[Steven G]

!5 from small and 45 from large. Compare these numbers.


9 from small and 27 from large. Compare these numbers.

 

[HallsofIvy]

I am in Year 10 and we are doing probability.

There are two hospitals in a certain town: a small one and a large one. In the small hospital, an average of 15 babies are born each day; in the large hospital, an average of 45 are born each day. Assume that the likelihood of giving birth to a boy is 50%.
In the small hospital, a record has been kept of the days (call them “small blue days”) during the year 2013 on which more than 9 boys were born. In the large hospital, a record has been kept of the days (“large blue days”) in 2013 on which more than 27 boys were born. How does the number of small blue days compare to the number of large blue days?

Proposition A: The expected number of small blue days is equal to the expected number of large blue days.

Proposition B: The expected number of small blue days is not equal to the expected number of large blue days.

You say "In the small hospital, a record has been kept of the days (call them “small blue days”) during the year 2013 on which more than 9 boys were born. In the large hospital, a record has been kept of the days (“large blue days”) in 2013 on which more than 27 boys were born." Since "more than 27" includes "more than 9" is a "large blue day" also a "small blue day" or did you mean "more than 9 but not not more than 27"? And what about there being 9 or fewer boys born on a given day? Are you not considering that case?

 

[Dr.Peterson]

I am in Year 10 and we are doing probability.

There are two hospitals in a certain town: a small one and a large one. In the small hospital, an average of 15 babies are born each day; in the large hospital, an average of 45 are born each day. Assume that the likelihood of giving birth to a boy is 50%.
In the small hospital, a record has been kept of the days (call them “small blue days”) during the year 2013 on which more than 9 boys were born. In the large hospital, a record has been kept of the days (“large blue days”) in 2013 on which more than 27 boys were born. How does the number of small blue days compare to the number of large blue days?

Proposition A: The expected number of small blue days is equal to the expected number of large blue days.

Proposition B: The expected number of small blue days is not equal to the expected number of large blue days.

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The problem is rather confusing, as it is easy to miss that we are talking about the distributions of births in two different hospitals. I think you are expected to compare these two distributions, observing that the mean for the large hospital is 3 times that for the small hospital, and that 27 is 3 times 9. Both distributions are assumed to be binomial, with the same p but different n.

Can you make a conclusion based on that?