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Probability question

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cultrara
Posts: 5147 - Karma: 46,850
A computer salesman sells a computer to 16 of his customers. If he
has 8 customers in a day, what is the probability he sells at least 3
computers?

Anyone have any idea how to do this? +k for any help
Feb 16 2012 3:05PM
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feihlination
Posts: 8356 - Karma: 1,084
i am pretty sure that there is something missing or worded wrong/ambigously
Feb 16 2012 3:13PM
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theJones
Posts: 676 - Karma: 158
is that the whole question?
Feb 16 2012 3:13PM
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LivingColour
Posts: 1134 - Karma: 21
this, OP your missing information
Feb 16 2012 3:14PM
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feihlination
Posts: 8356 - Karma: 1,084
i assume he sells a computer once every 16 customers

so its (via excel) a binomial thingy with p = 1/16, x=3 and tries is 8.

0,00990112 or pretty much 1%.
Feb 16 2012 3:14PM
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Casual.
Posts: 1125 - Karma: 28
the post above mine is probably what you're looking for, the question as it is is unanswerable in it's current state.
Feb 16 2012 3:31PM
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cultrara
Posts: 5147 - Karma: 46,850
16% not 16 customers sorry about that
Feb 16 2012 8:27PM
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feihlination
Posts: 8356 - Karma: 1,084
at least means NOT 0,1,2

the cumulative probability of 2 is 0,8774

1 minus that is the probability you want.
Feb 16 2012 8:32PM
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El.Guapo
Posts: 2139 - Karma: 3,173
multiply 8 by. 16 then divide by 3
Feb 16 2012 8:36PM
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feihlination
Posts: 8356 - Karma: 1,084
serious? so the probability of him selling at least one would be 128% or wat?
Feb 16 2012 8:55PM
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soulskier
Posts: 17806 - Karma: 3,841
it's probable, more than possible for sure
Feb 16 2012 8:59PM
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NSwidow
Posts: 888 - Karma: 3,222
In Australia, you dont have to do math in yr 11 and 12. I took full advantage of this. While everyone was in Maths, i was in the McDonalds drive thru line. So i can't help you. But i agree with everyone else. there is information missing. It's stupid.
All the maths you need to know is:

An average lap of the park is 11 minutes.
The lift line is an average of 3 minutes.
The lift takes 6 minutes.
You have 3 hours of skiing, without breaks.
On average, how many park laps can you do?
Feb 16 2012 8:59PM
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El.Guapo
Posts: 2139 - Karma: 3,173
16% of 8 is 1.28. divide 1.28 by 3 and you get 0.426666
Feb 16 2012 9:04PM
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Mr.Gaga
Posts: 2021 - Karma: 542

Probability you sell 0 computer with 8 clients are:

[0,84 x 0,84 x ... repeat 8 times] x 1 possible combinaisons   = 1x(0,84)^8 = 0,2479 (24,79%)


Probability you sell 1 computer with 8 clients are:

[0,16 x 0,84 x ... repeat 7 times]x 8 possible combinaisons  = 8x0,16x(0,84)^7 = 0,3777 (37,77%)


Probability you sell 2 computer with 8 clients are:

[(0,16)^2 x (0,84)^6] x 28 possible combinaisons = 0.2518 (25,18%)


Probability you sell more then 3 are:

1-(0,2479+0,3777+0,2518) = 0,1226 (12,26%)







**More details:

Possibles combinaisons of selling 0 computer are like (1=computer sold, 0= computer not sold for 1st to last client):

(00000000) (1 possibility)

For 1 computer:

(10000000), (01000000), (00100000), ... (8 possibilities)

For 2 computers (you can do a tree diagram to see it's 7+6+5+4+3+2+1=28 possibilities):

(11000000), (10100000), (10010000), ...
(01100000), (01010000), (01001000), ... (00000011)

So there are 28 ways of selling 2 computers to 8 clients and probabilities it happen are all (0,16^2)x(0,84^6).

There's 28 ways (combinaisons) to compute:

0,16 x 0,16 x 0,84 x 0,84 x 0,84 x 0,84 x...
0,16 x 0,84 x 0,16 x 0,84 x 0,84 x 0,84 x...
0,16 x 0,84 x 0,84 x 0,16 x 0,84 x 0,84 x...
0,84 x 0,84 x 0,84 x 0,16 x 0,16 x 0,84 x...

Those are the 28 ways of selling 2 computers in a day.

Feb 16 2012 11:56PM
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PJS.
Posts: 11943 - Karma: 895
Math is hard.
Feb 16 2012 11:58PM
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EastCoast315
Posts: 3136 - Karma: 137
Utterly pointless...
Feb 16 2012 11:58PM
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chicken
Posts: 6843 - Karma: 2,123
This can be done with the binomial distribution since there are a fixed number of trials, there are two outcomes, the trials are independent and the probability of success is constant from trial to trial.

Click for larger image

remember that the first term in that summation is "n choose x" on my calc the button is labeled "nCr". Also I accidentally put 6 choose x on the second line, but calculated it correctly with 8 choose x below, so that should be the correct answer.

Let me know if you are still confused.

Feb 17 2012 1:19AM
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blackmamba.
Posts: 969 - Karma: 56
couple of people have already posted the answer, but yeah, it's 12.26%.
Feb 17 2012 8:26AM
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El.Guapo
Posts: 2139 - Karma: 3,173
wrong.
Feb 17 2012 9:29AM
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blackmamba.
Posts: 969 - Karma: 56
one thing is for certain it aint 42.67%. that's way too high to make any logical sense

plug the values in here and check the last output


Feb 17 2012 9:40AM
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chicken
Posts: 6843 - Karma: 2,123
that is wrong for two reasons. number one because he later stated that the probability is 0.16 not 1/16. The other reason is because he only calculated the binomial probability for X=3 not the cumulative probability for X>2
Feb 17 2012 11:42AM
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cultrara
Posts: 5147 - Karma: 46,850
this was the correct answer.

thanks for the help guys, 10/10 for everyone who helped get it right.
Feb 17 2012 11:54AM
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El_Barto.
Posts: 11661 - Karma: 24,364
stats was the weirdest math i ever took. it was so simple yet gave so many people headaches. alas that knowledge left me immediately after 244
Feb 17 2012 1:22PM
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An10a_Eng
Posts: 2505 - Karma: 26
didnt look at the numbers but he is definitely right that its a binomial distribution...so thats enough for me to say hes right seeing as hes obviously taken a prob course before.
Feb 17 2012 2:50PM
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