Tria had one each of five different-shaped number solids having 4, 6, 8, 12, and 20 sides. She rolled two at a time and found probabilities for the sum of the numbers that came up. She recorded the probabilities in the first column of the table. When it came time to fill in the second column, she had forgotten which number solids she had used. Figure out which number solids she must have used and explain your thinking. The first one has been done. She found out that the probability of 4 is lesser than 5, which combinations did she use?

the answer   is 200

step-by-step explanation:

this is a problem about poisson probabilities.   i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.  

here's how you can see a poisson distribution coming.   when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution.   this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot.   there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything.   the form of the distribution is

  probability of n chips = {[e^(-x)]*(x^n)} / (n! )

5050

hope this !