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Help : AS Binomial Distribution Homework Question

Question 3 and 4 on my homework are very similar. I'm just wondering if there is quick way to work this out or do I have to work out the probability of every possible outcome to find the most likely one?
image-986e4abd-c264-449f-9c83-8bf0d9f8b64e4342710544516097610-compressed.jpg.jpeg
(edited 5 years ago)
Reply 1
Avatar for Notnek
Notnek
21
Original post by niclawrence01
Question 3 and 4 on my homework are very similar. I'm just wondering if there is quick way to work this out or do I have to work out the probability of every possible outcome to find the most likely one?
image-986e4abd-c264-449f-9c83-8bf0d9f8b64e4342710544516097610-compressed.jpg.jpeg

There's no need to check every possible outcome. It will be close to the mean so just check values around np to find the one with the largest probability.

There is a formula for the mode but you don't need to know it for A Level. It's not too hard to check a few values on your calculator (and the "list" mode will speed things up if you like).
The mean of what?
The values most likely would be around the expected frequency, which is found by calculating n x p.
By using the list function you may be able to compare these quicker and more efficiently.
Reply 4
Avatar for Notnek
Notnek
21
Original post by niclawrence01
The mean of what?

The mean of a binomial distribution X is equal to np where X~B(n, p).

E.g. if you roll a dice 60 times and the number of 6's is X then X~B(60, 1/6) and the mean number of 6's will be 60 x 1/6 = 10 which makes sense.

So for X~B(12, 0.4), the mean is 12 x 0.4 = 4.8 so just check values like 4, 5 on your calculator to find the one with the highest probability.
(edited 5 years ago)
Original post by Davidgray02
The values most likely would be around the expected frequency, which is found by calculating n x p.
By using the list function you may be able to compare these quicker and more efficiently.


So for question 3, do 12x0.4 which is 4.8 then what?
Well, as its binomial it as to be a whole number, so check the probability that X=5 and X=4 and see which one is largest.
Original post by Notnek
The mean of a binomial distribution X is equal to np where X~B(n, p).

E.g. if you roll a dice 60 times and the number of 6's is X then X~B(60, 1/6) and the mean number of 6's will be 60 x 1/6 = 10 which makes sense.

So for X~B(12, 0.4), the mean is 12 x 0.4 = 4.8 so just check values like 4, 5 on your calculator to find the one with the highest probability.


Omg ok that makes sense now! Thanks so much
Reply 8
Avatar for Notnek
Notnek
21
Original post by niclawrence01
So for question 3, do 12x0.4 which is 4.8 then what?

So the mode will be a value near there like 4 or 5. Check those values for the one with the highest probability.
Original post by Davidgray02
Well, as its binomial it as to be a whole number, so check the probability that X=5 and X=4 and see which one is largest.


Thanks! I get it now

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