The Hospital Question

missy_muffett

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Another probability question: I think Hospital A would have more boys born on one day, because of the number of births.

There are two hospitals in a large city. Hospital A has, on average, 50 births a day. Hospital B has, on average, 10 births a day.
Which hospital is more likely to have 80% or more boys born on one day?

  • Hospital A
  • Hospital B
  • They are both equally likely
Give your answer and explain your reasoning on the board.
 
Another probability question: I think Hospital A would have more boys born on one day, because of the number of births.

There are two hospitals in a large city. Hospital A has, on average, 50 births a day. Hospital B has, on average, 10 births a day.
Which hospital is more likely to have 80% or more boys born on one day?

  • Hospital A
  • Hospital B
  • They are both equally likely
Give your answer and explain your reasoning on the board.
How did you calculate that?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/for
 
Another probability question: I think Hospital A would have more boys born on one day, because of the number of births.

There are two hospitals in a large city. Hospital A has, on average, 50 births a day. Hospital B has, on average, 10 births a day.
Which hospital is more likely to have 80% or more boys born on one day?

  • Hospital A
  • Hospital B
  • They are both equally likely
Give your answer and explain your reasoning on the board.

I'm not even quite sure what "80% or more boys born on one day" means!

I suppose it is asking, for which hospital the probability that at least 80% of the births on a given day are boys is greater. Does that sound right to you?

Note that it is asking about a percentage, not an absolute number, so the number of births is not directly relevant.

When you tell us your ideas about the problem (not just what your answer is, but why), please tell us what you have learned that you think is relevant. Since this is a question that is asking for a conclusion without giving you a lot of specifics, I expect that they have given you some examples from which you are expected to see a basic principle to apply. It will help if you tell us what principles have been discussed, and/or what examples were used.
 
Note that it is asking about a percentage, not an absolute number, so the number of births is not directly relevant.

Except, doesn't the law of large numbers work against you a bit more, in the case of the hospital with a higher birth rate? ;)
 
Except, doesn't the law of large numbers work against you a bit more, in the case of the hospital with a higher birth rate? ;)

Yes, the law of large numbers is relevant, as is the binomial distribution, and various ideas related to sampling. Any of those might be what was discussed in the class.

I wasn't saying there's no effect, only that it's not as simple (direct) as was implied by talking about the number of boys born being greater.
 
Another probability question: I think Hospital A would have more boys born on one day, because of the number of births.

There are two hospitals in a large city. Hospital A has, on average, 50 births a day. Hospital B has, on average, 10 births a day.
Which hospital is more likely to have 80% or more boys born on one day?

  • Hospital A
  • Hospital B
  • They are both equally likely
Give your answer and explain your reasoning on the board.
I think that you should Give your answer and explain your reasoning on the board
Consider tossing a coin 10 times vs 10,000 times. It is more likely that you get at least 8 heads out of 10 tosses then at least 8000 out of 10000 tosses. The more tosses you make the closer you will get to 50% of heads.
Now go and do your work and show it to us.
 
The hospital question

The reason I choose hospital 'A' was because they have on average 50 births a day, compared to hospital 'B', which has 10 births a day.
Therefore, I thought the chances of more boys being born in hospital 'A' was because of the number of births. I also think there are more
boy babies born compared to girl babies.
 
The reason I choose hospital 'A' was because they have on average 50 births a day, compared to hospital 'B', which has 10 births a day.
Therefore, I thought the chances of more boys being born in hospital 'A' was because of the number of births. I also think there are more
boy babies born compared to girl babies.
Ahh, that the problems. Birth of boys and girls are basically 50-50.
Of course if you have more birth in one hospital over another, then the hospital with more births will (in the long run) have more boys than the smaller hospital. But you were not asked which hospital will have more boys. You were asked which hospital has a better chance of having 80% or more boys.

Again, if you tossed a FAIR coin one million times would you really expect 80% of the tosses to be heads? Might it happen more easily if you only tossed a coin 5 times (that is only 4 heads out of 5)?
 
The reason I choose hospital 'A' was because they have on average 50 births a day, compared to hospital 'B', which has 10 births a day.
Therefore, I thought the chances of more boys being born in hospital 'A' was because of the number of births. I also think there are more
boy babies born compared to girl babies.

But the question is not about "more boys being born in A", it is about a greater probability that at least 80% of the births at A are boys. It is essential to read these problems carefully.

Have you looked at what has been discussed? I mentioned several things you might have learned about: "the law of large numbers, ... the binomial distribution, and various ideas related to sampling". Do any of those sound familiar?

Others have suggested related ideas: "Consider tossing a coin 10 times vs 10,000 times. It is more likely that you get at least 8 heads out of 10 tosses then at least 8000 out of 10000 tosses." That is an example of the law of large numbers: for a large sample (that is, if you repeat something many times), the actual fraction of "successes" will be increasingly close to the "theoretical probability". That is, with more births, the actual percentage will be closer to 50%.

Again, does that sound like something you have read?
 
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