My Math Forum How to calculate this kind of probability?

 December 26th, 2011, 03:11 AM #1 Newbie   Joined: Dec 2011 Posts: 4 Thanks: 0 How to calculate this kind of probability? Here's the question: A restaurant serves 8 burger, 12 steak, and 10 fried chicken. If the customer who comes to the restaurant is randomly chosen, calculate the probability of 2 from the next 4 customers will buy burger? Thanks for helping me.
 December 26th, 2011, 08:06 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: How to calculate this kind of probability? What's the chance of ordering a burger? What's the chance of ordering a non-burger? Now use the binomial distribution.
 December 26th, 2011, 03:01 PM #3 Newbie   Joined: Dec 2011 Posts: 4 Thanks: 0 Re: How to calculate this kind of probability? I don't know what to do ...I am still confused... The chance ordering burger = 8/30 Non burger = 22/30 Is it right??? but I don't know next....
 December 27th, 2011, 12:28 AM #4 Newbie   Joined: Dec 2011 Posts: 4 Thanks: 0 Re: How to calculate this kind of probability? I try to calculate that the probability of choosing burger = 8/30 so, if there are 2 from 4 customer, probability to choose burger = 2/4 * 8/30 = 4/30 = 2/15. I don't know it is right or wrong...cz I calculate it so simple.... or maybe it needs combinatoric formula... I don't know what I have to do...
 December 27th, 2011, 02:54 AM #5 Senior Member   Joined: Apr 2011 From: USA Posts: 782 Thanks: 1 Re: How to calculate this kind of probability? If there's 2 people going to get a burger, that's (8/30)(8/30). Then the other 2 people would be non-burgers, so (22/30)(22/30). Then times the possible ways two people could be the burger-buyers. You were already told to use the binomial. Do you not have this equation? $\binom{n}{x}p^x(1-p)^{n-x}$ $\binom{4}{2}\left(\frac{3}{30}\right)^2\left(\frac {22}{30}\right)^2$ (I am assuming the number of burgers, steak and chicken is what they sell on average.) You aren't taking into consideration the 2 people not buying burgers, nor that the 2 who buy them can be 6 different combinations of people.

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