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statistics - i need to know what methods to use. (:?

1. on average 1 in 20 members of the population of this country has a particular DNA feature. members of the population are selected at random until one is found who has this feature.
find the probability that the first person to have this feature is:
a)the sixth person selected
b)not among the first ten people

c)find the expected number of people selected.



2. an examination paper consists of 8 questions, of which one is geometric distribution and one is binomial distributions.
i)if the 8 questions are arranged in a random order, find the probability that the questino on geo.distributions is next to the question on bino.distributions. )

ii)four of the questions including the one on geo distributions are worth 7 marks each and the remaining four questions including the one on bino distribuitons are worth nine marks each. the 7 mark questions are the first four questions on the paper but arranged in a random order. the 9 mark questions are the last four on the paper but arranged in a random order. find the probability that
a)the questions on geo distributions and bino.distributions are next to one another.
b) the questions on geo distributions and bino. distributions are seperated by at least 2 other questions.



sorry the questions are so long - i'm unsure of which methods to use. any suggestions/help? :smile: thanks
Reply 1
Write the probabilities:

first person has it 0.2
second person and not first 0.8*0.2
third, not first or second 0.8^2*0.2

Do you recognise the distribution?
Reply 2
Ouch, you're in a lot of trouble if you can't recognise these. All you need to know is that if there is a set number (I.e in a sample of 20 people) it's geometric, if it's not, then it's binomial. Google for the other properties of the two distributions.
Reply 3
Coda
Ouch, you're in a lot of trouble if you can't recognise these. All you need to know is that if there is a set number (I.e in a sample of 20 people) it's geometric, if it's not, then it's binomial. Google for the other properties of the two distributions.



we've hardly done any stats at college.
they just tried to cram it all in over the last couple of weeks :|
Reply 4
rnd
Write the probabilities:

first person has it 0.2
second person and not first 0.8*0.2
third, not first or second 0.8^2*0.2

Do you recognise the distribution?



no :s-smilie:
i swear we havent done anything about distributions and stuff. :/
Reply 5
OK. You can still work it out. The one I gave a hint for is a geometric distribution which you can look up if you like.

You don't really need to though. If the first person with it is the 6th person checked you are looking for P(first 5 don't have it and 6th person does) = 0.8^5*0.2
Reply 6
rnd
OK. You can still work it out. The one I gave a hint for is a geometric distribution which you can look up if you like.

You don't really need to though. If the first person with it is the 6th person checked you are looking for P(first 5 don't have it and 6th person does) = 0.8^5*0.2



is that all you have to do?
so for the one where its not in the first ten - its 0.8^10x0.2?
Reply 7
rdftw
is that all you have to do?
so for the one where its not in the first ten - its 0.8^10x0.2?


No. If it's not in the first ten it happens later. It's 1-P(it's one of the first 10). I make it 0.1064.

For the last part you need to know (or work out) that the mean of a geometric distibtution (starting at 1) is 1/p so in your case it's 1/0.2=5
Reply 8
rnd
No. If it's not in the first ten it happens later. It's 1-P(it's one of the first 10). I make it 0.1064.

For the last part you need to know (or work out) that the mean of a geometric distibtution (starting at 1) is 1/p so in your case it's 1/0.2=5



oh okay, - and is that the answer?
you just have to do 1/prob so the answer is 5?
thanks


oh and how come its 0.2 when its 1/20? should it not be 0.05? :s-smilie:
Reply 9
May I ask what course you're studying. You still have a lot of questions that need answering and you don't seem to have the teaching you should have had.
Reply 10
rnd
May I ask what course you're studying. You still have a lot of questions that need answering and you don't seem to have the teaching you should have had.


ocr as maths.
c1 c2 s1
rdftw
is that all you have to do?
so for the one where its not in the first ten - its 0.8^10x0.2?



The formula you have there is for "not in the first ten" and "it's the eleventh".

Well, you're not interested in the 11th, nor in anything after the 10th.

So the probability of not being in the first 10 is just 0.8^10 = 0.1074 (4 dec. pl.)
Reply 12
I believe ghostwalker is right. Please ignore my post on part b. Sorry.

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