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Urgent: Maths CIE Stats

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cs:
June 2010 Q1,

how do you know if that question is asking for binomial or P and C..?

A bottle of sweets contains 13 red sweets, 13 blue sweets, 13 green sweets and 13 yellow sweets. 7 sweets are selected at random . Find the probability that exactly 3 of them are red.

My first instinct is to do X~B (7, 13/52)
and then P(x=3) then continue,

but the answer is found using 13C3 X 39C4  over 52C7

anyone can help me?

Deadly_king:

--- Quote from: cs on October 22, 2010, 03:10:49 am ---June 2010 Q1,

how do you know if that question is asking for binomial or P and C..?

A bottle of sweets contains 13 red sweets, 13 blue sweets, 13 green sweets and 13 yellow sweets. 7 sweets are selected at random . Find the probability that exactly 3 of them are red.

My first instinct is to do X~B (7, 13/52)
and then P(x=3) then continue,

but the answer is found using 13C3 X 39C4  over 52C7

anyone can help me?



--- End quote ---

Nope.......you cannot use binomial here. This is because you don't even now what are the colours of the selected sweets. So you cannot take if fro granted.

Moreover the word exactly gives you a hint that you should be using combinations since the selected sweets must be 3 red and the rest a ny other colour.

So firstly, the probability of 3 red ---> 13C3

Since you have been told that there is exactly 3 red and not more, this implies that the rest(4) should be of other colours out of only 39 sweets ---> 39C4

Since you are finding probability, you should divide the above product by the probability of taking out 7 sweets = 52C7

Hence the solution is (13C3 x 39C4)/52C7

cs:
Thank you Deadly King, you are always here to solve my doubt.. =)

mousa:
I would like to add more, the probability of success in " choosing a red sweet " is NOT constant, it keeps on changing everytime you make a selection since the sweets are not replaced. Furthermore, the trials aren't independent. Both of those conditions are essential for binomial distribution.

hope that helped, by the way, your doing your exam in this nov session??

Deadly_king:

--- Quote from: cs on October 22, 2010, 05:58:57 am ---Thank you Deadly King, you are always here to solve my doubt.. =)

--- End quote ---

Anytime dear :)

By the way when are you having your stats exams ??? 3 Nov ???

Thanks for your info mate :D
Very much appreciated :)

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