BINOMDIST maths question help please!

[Charlie52]

Any help on which values to input into the formula would be very much appreciated! Heres the question;

Catering for 16 people you provide 4 vegetarian and 12 non-vegetarian meals. (You assumE that the probability someone is a vegetarian is 4/16 ie 0.25) What is the probability that you will have at least one disappointed guest?

So far i have figured: =BINOMDIST(15,16,0.5,TRUE) but have no confidence in these values as being right, a little help please!!
Thank you!

 

[AhoyNC]

@ Ahoy:

What is the probability that exactly four vegetarians show up?

How many people are disappointed in that case?

Does that agree with your calculation of 98.9%

SHG
If exactly 4 show up no one is disappointed or 0%.
However that is not what this question is asking.
The question is:
What is the probability that you will have at least one disappointed guest?
Not how many veg. are going to show up.
The combination formula that is in the binomial distribution formula takes are of that for us.

The binomial probability distribution formula is:
P(x)=nCx π^x (1-π)^n-x
where:
C is the combination formula.
n is the number of trials
x is the random variable (number of successes)
π is the probability of sucess for each trail
This problem fits the binomial probability because 4 things must be true:
1. Outcome of each trail must be classified as either a sucess or failure. In this case a sucess is not having a veg. meal.
2. Must have a fixed number of trials - 16 here.
3. Probability must stay the same for each trial - always .25 in this case.
4. Trials need to be independent.

 

[shg]

If exactly 4 show up no one is disappointed or 0%.

Right, and what's the probability of that happening?

And would you agree that if anything other than that happens, someone is disappointed?

So what's the probability of at least one person being disappointed?

 

[AhoyNC]

shg
No what we are saying is that as we take each persons order there is a 25% chance that they will order a veg. meal and 75% change they will order meat. Then based on those probabilities what is the probability that one or more people will be disappointed.
This is a standard type question you will find in any intro. applied statistics textbook. It is designed to see if the student can recognize a binomial distribution problem and apply the right formula.

Charlie57 stated that he had to use the binomdist function to solve the problem. He was on the right track he just needs to subtract his answer from 1.

The way Excel calulates this if you were looking for the probability that 4 or less people would be disappointed you could use the formila as is. If you need to know the probability that 5 or more people would be disappointed then you have to use the formula to find the number for 4 or less and subtract from one as shown in my post above.

 

[shg]

Going back to post#4,

The probability that exactly 4 vegetarians show up is =BINOMDIST(4, 16, 0.25, FALSE) ~ 22.5%

The chance of any other number showing up, and therefore one or more people being disappointed, is =1 - BINOMDIST(4, 16, 0.25, FALSE) ~ 77.5%, not 98.9%

 

[xenou]

I think it's undefined whether a meat-eating guest would be "disappointed" if they have to eat vegetarian meal. This affects the outcome since less than four vegetarians is okay if meat eaters don't mind vegetarian meals, but it results in a disappointed guest if meat eaters are disappointed by having a vegetarian meal. The former is the cumulative probability of having 5 or more veggie guests and the latter is the probability of not having exactly four vegetarian guests. [Edit - e.g. ~77.5% as in shg's last post]

 

[shg]

If carnivores weren't disappointed to be relegated to eating roots and flowers, then you'd just order all veggie meals and everyone would always be happy.

 

[xenou]

I happen to quite like many vegetarian dishes so - so perhaps this is a trick question since we can have 100% satisfied diner's 100% of the time.

Yum...

<img width="228" height="148" src="http://www.ecosalon.com/wp-content/uploads/2009/01/veggie-pizza.jpg"/>

 

[shg]

So you get served a pizza with all that ... stuff ..., while the guy next to you has one loaded with sausage and pepperoni. There's a good chance you'd physically assault the guy.

 

[Charlie52]

Thank you for all your thoughts guys!! And in fact in small print I am told that meat eaters do not enjoy the veggie option!