Let's say we have 4 shapes (triangle, square, rectangle and circle) and 50 people are each asked to pick 1 of the four shapes. Based on statistics, it is said that half of the people (25) will select a triangle and the number of people who select a rectangle is twice the number who choose square. Finally, if we're told that 30 people selected either triangle or square, 15 picked rectangle and 5 chose circle. Given this information, what's the ratio of triangle to square selection (among 30 people who picked one or the other).
I tried to set up variables and divide, but was not successful:
let p = total number of people 0.5p = triangle
n = # who like square 2n = rectangle
So,
2n = 15 n = 7.5
This doesn't make sense as n (which is the number of people who like square) isn't a whole number.
I explored Maximum Likelihood Estimation as well as Expectation Maximization, but don't see how it could be applied here. How can I solve this?
The data you are given are inconsistent. We are told $30$ selected triangle or square, $15$ chose rectangle, and $5$ chose circle. This adds nicely to $50$. As we were told $25$ chose triangle, $5$ chose square, which is inconsistent with twice as many choosing rectangle as square.