# Binomial expansion question

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#1
Can somebody plz explain what I need to do for part c below.
I'm guessing there's an alternative to drawing 7 branches of a probability tree.
Thanks
Last edited by Rhys_M; 1 month ago
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1 month ago
#2
Each experiment is either rolls 4 primes or not. He does seven of them and you want to find the probability that it occurs twice. Does that sound familiar?
Last edited by mqb2766; 1 month ago
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#3
(Original post by mqb2766)
Each experiment is either rolls 4 primes or not. He does seven of them and you want to find the probability that it occurs twice. Does that sound familiar?
Yea that's the question - but no i can't figure out what to do. Is it something to do with the number of combinations of it happening twice x the probability of it happening twice ?
If so how many combinations are there?
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1 month ago
#4
(Original post by Rhys_M)
Yea that's the question - but no i can't figure out what to do. Is it something to do with the number of combinations of it happening twice x the probability of it happening twice ?
If so how many combinations are there?
re-read mqb2766's hint carefully - you have seven trials i.e. a fixed number of trials. Each trial can be 4 primes ("success") or not ("failure"). There is a fixed probability of "success" which you calculated earlier. Does this ring any bells?
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#5
(Original post by Rhys_M)
Yea that's the question - but no i can't figure out what to do. Is it something to do with the number of combinations of it happening twice x the probability of it happening twice ?
If so how many combinations are there?
(Original post by mqb2766)
Each experiment is either rolls 4 primes or not. He does seven of them and you want to find the probability that it occurs twice. Does that sound familiar?
Oh shoot no its just another binomial isnt it
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1 month ago
#6
Yeah this is X~B(n,p) and the assumptions will just be stuff like the dice being fair
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1 month ago
#7
Yes. Thats one reason why they asked you the properties of the (binomial) distribution at the start.

Tbh, its a reasonably common question structure where they describe a new "binomial" question part at the end of the question where the new distribution defined in terms of a yes/no - type outcome from the original distribution. Part b) even got you to calculate the p in the new binomial distribution. Again, a fairly clear hint.
Last edited by mqb2766; 1 month ago
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1 month ago
#8
When it asks for assumptions, just state the standard stuff -- fixed chance of success, independent trials and fixed number of trials. And yes, this is just standard binomial distribution.
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