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# Probability watch

1. In a study conducted by UCLA, it was found that 25% of college freshmen support increased military spending. If 6 college freshmen are randomly selected, find the probability that:
Fewer than 4 support increased military spending

Can anybody help me out here? It would be much appreciated. Thanks in advance.
3. In a study conducted by UCLA, it was found that 25% of college freshmen support increased military spending. If 6 college freshmen are randomly selected, find the probability that:
Fewer than 4 support increased military spending

Can anybody help me out here? It would be much appreciated. Thanks in advance.
As with all probability questions begin by analysing the text. First clue - find the probability that Fewer than 4 support increased military spending

i.e. what is the probability that 0,1,2 or 3 freshmen support increased military spending.

Now think about how to get these outcomes, and how many times we can get them. The easiest is no people supporting the increased spending (P(0)): this is simply

assuming that each answer is independent of all the others. There is only one way to get this - everybody says they aren't in favour.

Now consider P(1), the probability for only 1 person of the 6 supporting the increased spending. This is given by

as there are 6 different ways to get that 1 person is in favour (e.g. person 1 says yes, all others say no, or person 2 says yes, all others say no etc.)

This type of probability can be modelled by the binomial distribution, with the following equation

where k is the number of sucesses (i.e in this case people agreeing with the spending), n is the sample size (i.e. 6) and p is the probability of success (in this case 0.25)

As with all probability questions begin by analysing the text. First clue - find the probability that Fewer than 4 support increased military spending

i.e. what is the probability that 0,1,2 or 3 freshmen support increased military spending.

Now think about how to get these outcomes, and how many times we can get them. The easiest is no people supporting the increased spending (P(0)): this is simply

assuming that each answer is independent of all the others. There is only one way to get this - everybody says they aren't in favour.

Now consider P(1), the probability for only 1 person of the 6 supporting the increased spending. This is given by

as there are 6 different ways to get that 1 person is in favour (e.g. person 1 says yes, all others say no, or person 2 says yes, all others say no etc.)

This type of probability can be modelled by the binomial distribution, with the following equation

where k is the number of sucesses (i.e in this case people agreeing with the spending), n is the sample size (i.e. 6) and p is the probability of success (in this case 0.25)

So when it comes to getting less than 4 people who will agree, how do I input this into the formula? What is the value of k considering it can either be 1, 2 or 3? Do I have to repeat it 3 times and add them or something?
5. (Original post by IsThisLife???)
So when it comes to getting less than 4 people who will agree, how do I input this into the formula? What is the value of k considering it can either be 1, 2 or 3? Do I have to repeat it 3 times and add them or something?
the means that you work out the right hand formula for k = 0, 1, 2, 3, and add them up.
6. So when it comes to getting less than 4 people who will agree, how do I input this into the formula? What is the value of k considering it can either be 1, 2 or 3? Do I have to repeat it 3 times and add them or something?
Its a sum over the values of k from 0 to 3, i.e.

So explicitly you do

Is that a bit clearer?
Its a sum over the values of k from 0 to 3, i.e.

So explicitly you do

Is that a bit clearer?
OK thanks, but is there no shortcut? If I k was less than 100 is there no quicker way other than repeating the formula 99 times and then adding it up?
8. OK thanks, but is there no shortcut? If I k was less than 100 is there no quicker way other than repeating the formula 99 times and then adding it up?
Not that I know of for a binomial distribution directly. I guess if it was like k<100 you'd approximate it to a normal distribution and use integration to find the probability. If this is a practical problem then you could write a piece of code to run through the values of k and sum them, would be done in a second then!
9. 0.9624
Not that I know of for a binomial distribution directly. I guess if it was like k<100 you'd approximate it to a normal distribution and use integration to find the probability. If this is a practical problem then you could write a piece of code to run through the values of k and sum them, would be done in a second then!
OK thanks. You obivously have a good understanding of statistics. I'm doing pure Economics at Uni and having only done Mechanics 1 & 2 at A level I have no experience with statistics. In the course we are doing there are a couple of Statistics modules, so stuff like standard deviation and hypothesis testing are going to come up. Therefore, in your opinion, how difficult is it to grasp stats? What should I do to get a full understanding?
11. (Original post by ronaldo91)
0.9624
Yeah thats what I have arrived at. Thanks. I'm assuming you done it the way it has been suggested to me, using the formula for the value of k being 0, 1, 2, 3 & 4 and then adding them?
12. OK thanks. You obivously have a good understanding of statistics. I'm doing pure Economics at Uni and having only done Mechanics 1 & 2 at A level I have no experience with statistics. In the course we are doing there are a couple of Statistics modules, so stuff like standard deviation and hypothesis testing are going to come up. Therefore, in your opinion, how difficult is it to grasp stats? What should I do to get a full understanding?
Stats can definitly be tricky and im not fan of it myself - I always try to turn the questions into pure maths type questions which I can answer more easily... To be honest best thing is probably to give a textbook on statistics for economists a look, or somewhere like here

http://www.economicsnetwork.ac.uk/te...economists.htm

perhaps?

Sorry I cant be more helpful on this point, but im actually a physicist so don't know much other than the more basic stuff!
13. (Original post by IsThisLife???)
Yeah thats what I have arrived at. Thanks. I'm assuming you done it the way it has been suggested to me, using the formula for the value of k being 0, 1, 2, 3 & 4 and then adding them?
you mean k 0 to 3 (since less than 4)

basic method is adding it all up individually because it's a binomial distribution (fixed prob, success/fail, fixed n trials) worked out by combinations of failure/success for each k.

but I had an s1 book nearby (did the exam in jan) and just looked up the table for cumulative binomial distribution. (this is the shortcut method you seek)

But do it the proper way to get a full understanding
14. Couldn't you use cdfgeo(6,0.25,4)

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