during the school year jose jamal and jane can buy hot lunch or salad bar in the school cafeteria or bring a lunch from home .They play the game to help them decide which kind of all of them will have the following school day. these are the rules for the game:
On a slip of paper each person writes a 1, 2 or 3 and turns their slip upside down.
On the count of three, each slip is turned over so all people can see it.
Add to find the total.
If the sum is 3, 4, or 5, all will buy a hot lunch. If the sum is 6 or 7, all will buy salad bar. If the sum is 8 or 9 all will bring a lunch from home.

Question

during the school year jose jamal and jane can buy hot lunch or salad bar in the school cafeteria or bring a lunch from home .They play the game to help them decide which kind of all of them will have the following school day. these are the rules for the game:
On a slip of paper each person writes a 1, 2 or 3 and turns their slip upside down.
On the count of three, each slip is turned over so all people can see it. 
Add to find the total. 
If the sum is 3, 4, or 5, all will buy a hot lunch. If the sum is 6 or 7, all will buy salad bar. If the sum is 8 or 9 all will bring a lunch from home.

anonymous · Answer

wow what a problem 
you have a lot of work to do

anonymous · Answer

how many elements in the sample space? i guess there are $3^3=27$ different possible combinations 
of those only 1 (3,3,3) gives a total of 9
how may give a total of 8? 
(3,3,2) (3,2,3) (2,3,3) are the only ones i can think of, so the probability you get a 9 is $\frac{1}{27}$ and the probability you get an 8 is $\frac{3}{27}$ for a total of 
$$\frac{4}{27}$$ as the probability you will bring lunch from home