Struggling with a maths probability question

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Yaboi_marky
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Lisa is part of the Maths club at college. This means that on Tuesdays, she gets to the college canteen 30 minutes after the start of the lunch break. She notices noticed that the probability that there are any chips left by the time she gets to the canteen on a Tuesday is 30%. She always has chips when they are available.

5 (a) By selecting and using an appropriate probability distribution, find the probability that Lisa will have chips on a Tuesday between 2 and 5 times in a term of 14 weeks. Fully justify your answer. [4 marks]

5 (b) Find the number of Tuesdays that Lisa will have chips on average. Fully justify your answer. [2 marks]

Can someone please help me with this question? it would be much appreciated
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mqb2766
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(Original post by Yaboi_marky)
Lisa is part of the Maths club at college. This means that on Tuesdays, she gets to the college canteen 30 minutes after the start of the lunch break. She notices noticed that the probability that there are any chips left by the time she gets to the canteen on a Tuesday is 30%. She always has chips when they are available.

5 (a) By selecting and using an appropriate probability distribution, find the probability that Lisa will have chips on a Tuesday between 2 and 5 times in a term of 14 weeks. Fully justify your answer. [4 marks]

5 (b) Find the number of Tuesdays that Lisa will have chips on average. Fully justify your answer. [2 marks]

Can someone please help me with this question? it would be much appreciated
What sort of a distribution might be appropriare?
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theprettyrainbow
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Its binomial distribution so uh X~B (14, 0.30) then all you have to do is solve p(2<x<5) you have to inlcude 2 and 5 as well!
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Yaboi_marky
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(Original post by mqb2766)
What sort of a distribution might be appropriare?
It says I need to use probability distribution but I'm not sure how to use it to find this answer. I tried making a table for all the different times she has chips from 1 to 14:

x 1 2 3 4 5 6 7 8 9 10 11 12 13 14
P(X=x) x/14*0.3
but that wasn't getting me anywhere
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mqb2766
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(Original post by Yaboi_marky)
It says I need to use probability distribution but I'm not sure how to use it to find this answer. I tried making a table for all the different times she has chips from 1 to 14:

x 1 2 3 4 5 6 7 8 9 10 11 12 13 14
P(X=x) x/14*0.3
but that wasn't getting me anywhere
Have you done binomial, poisson, ... What might be good here?
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Yaboi_marky
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(Original post by theprettyrainbow)
Its binomial distribution so uh X~B (14, 0.30) then all you have to do is solve p(2<x<5) you have to inlcude 2 and 5 as well!
I thought about doing it like that as well with the cumulative distribution function but then realised it wanted it with probability distribution instead, do you think it matters?
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Yaboi_marky
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(Original post by mqb2766)
Have you done binomial, poisson, ... What might be good here?
wait does "probability distribution" include binomial distribution because then I might be able to get it and also, I'm in year 12 so we haven't covered Poisson
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mqb2766
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(Original post by Yaboi_marky)
wait does "probability distribution" include binomial distribution because then I might be able to get it and also, I'm in year 12 so we haven't covered Poisson
Yes binomial distribution is correct.
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Yaboi_marky
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wait does the term "probability distribution" also include binomial distribution, because I thought they were two separate things
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mqb2766
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(Original post by Yaboi_marky)
wait does the term "probability distribution" also include binomial distribution, because I thought they were two separate things
Why?
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theprettyrainbow
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(Original post by Yaboi_marky)
I thought about doing it like that as well with the cumulative distribution function but then realised it wanted it with probability distribution instead, do you think it matters?
I don't exactly know how it would work with probability distribution not going to lie but binomial seems to be the option especially if this is a year 12 question. The only other distribution it could be is normal but it isn't that because there is no use of mean or standard deviation
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Yaboi_marky
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(Original post by mqb2766)
Yes binomial distribution is correct.
Ahh okay, let me try doing this with binomial distribution then
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Muttley79
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(Original post by Yaboi_marky)
wait does the term "probability distribution" also include binomial distribution, because I thought they were two separate things
The binomial is one of the 'named' probability distributions like Normal, Poisson - I think you are thinking of distributions defined in tables?
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Yaboi_marky
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(Original post by theprettyrainbow)
I don't exactly know how it would work with probability distribution not going to lie but binomial seems to be the option especially if this is a year 12 question. The only other distribution it could be is normal but it isn't that because there is no use of mean or standard deviation
I did it with binomial and did this

14C3 x 0.3^3 x 0.7^11 + 14C4 x 0.3^4 x 0.7^10

and got 0.42(3sf)

does that seem right? I thought because the question does not say "between 2 and 5 INCLUSIVE" that it only meant 3 and 4
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theprettyrainbow
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(Original post by Yaboi_marky)
I did it with binomial and did this

14C3 x 0.3^3 x 0.7^11 + 14C4 x 0.3^4 x 0.7^10

and got 0.42(3sf)

does that seem right? I thought because the question does not say "between 2 and 5 INCLUSIVE" that it only meant 3 and 4
I think that should be the answer. But if not then maybe 2 and 5 should be included
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Yaboi_marky
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(Original post by theprettyrainbow)
I think that should be the answer. But if not then maybe 2 and 5 should be included
okay then, Im gonna go with that, thanks all for all the help
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