David B. answered • 05/09/21

Math and Statistics need not be scary

This question can not be answered unless we make one major assumption - that all the probabilities are statistically independent.

If they are statistically independent than the P(A and B and C) = P(A) * P(B) * P(C), and so on.

Thus for Yellow & Blue & Red the probability = .8 x .6 x .75 or 0.36

For Yellow & Blue & Red & Green the probability = .36 x .65 or 0.234

For Yellow & Blue & Red & Green & Black the probability = .234 x .55 or 0.1287

For Yellow & Blue & Red & Green & Black & Grey the probability = 0.1287 x .70 or 0.09009

That is the answer to the question. The question said there was a survey of 6Million people, how many like certain colour combinaitons. The proportions above give that answer.

Although questions based on surveys are used to make predictions of the population represented by the survey and not the survey population itself (which is known and need not be estimated), it is implied here, however erroneously , that we are to predict the numbers of people in the survey have a certain trait, from the summary results of the survey! Under this artificial assumption we can put numbers on the combinations.

out of 6Million the numbers (assuming statistical independence) are:

Yellow, Blue, Red, Green, Black, Grey. = 540540

Yellow, Blue, Red, Green, Black = 772200

Yellow, Blue, Red, Green = 1404000

Yellow, Blue, Red = 2160000