uni probability question (1 Viewer)

[kfnmpah]

Ok so I am at uni doing a "working mathematically" course that focuses on problem solving.
The lecturer defined problem solving as a bunch of stuff, but what is relevant to this post is that he said 'you don't know a predetermined answer, you have to decide where to stop' so this is more of a hit-me-with-suggestions type thing than a solve it nao

A cereal manufacturer wants to increase sales by including a series of tokens in its cereal boxes. If there are 8 tokens in the series, how many cereal boxes would you be expected to buy to complete the set without swapping or trading

i was thinking about doing Random number generators for integers between (and inclusive of) 1 and 8 and doing IF functions in excel but that gets convoluted

Then i was thinking saying what is the probability of getting all 8 if you buy 10 boxes, if you buy 20 boxes etc and go up to whatever number until I get really really close to 1 but i *completely* forget how to do this. what would i do for this probability calculation?

 

[morts]

are all 8 in an equal ratio? or are some rarer than others?

 

[Shadowdude]

And do we assume every cereal box has a token?

 

[seanieg89]

Assuming each box contains a token and each token is equally likely, the expected number of boxes needed is about 21.74.

To do this, figure out the expected number of boxes needed to progress from owning k different tokens to owning (k+1) different tokens and add them up.

 

[kfnmpah]

help me

 

[kfnmpah]

I am seriously so dumb when it comes to this sort of stuff.

>doing a maths degree
>can't remember basic probability

k

 

[seanieg89]

Read this and adapt it http://mathforum.org/library/drmath/view/56653.html.

 

[kfnmpah]

see you stupid mods this is why we need rep

how am i meant to thank this guy for helping me? just SAY thank you? i need little green boxes to express my gratitude

 

[seanieg89]

see you stupid mods this is why we need rep

how am i meant to thank this guy for helping me? just SAY thank you? i need little green boxes to express my gratitude

haha its all good. by the way most of the things they ask you will have been asked before...if you ever get stuck just google the main parts of the problem and you will probably find something. you don't learn as much but its nice and fast.

 

[kfnmpah]

and what if the probabilities weren't uniform?

what if, say, the 8th token was distributed half as much as the first token?

so i did a difference equation and added up the expected number of trials to get a new token and i got 22boxes (21.74) but yeah what if it was like
P(1)=1/6
p(2)=1/8
P(3)=1/8
P(4)=1/8
P(5)=1/8
P(6)=1/8
P(7)=1/8
P(8)=1/12

how would i change my diffrence equation?

I've got
a=expected number of trials before new token
a=P(new token) + P(probability of getting 1+a)(1+a)
so for the first box, for example i have

a=7/8 + 1/8(1+a)
which gives a=8/7

end eventually i add up a through g and get 22 but yeah what if, say, i had the token distribution mentioned above????

 

[NWO]

Not an ap or a gp question.. lol