What would the formula be for this problem?

2/3

Step-by-step explanation:

The area of the entire circle = pi r^2

Area = 3.14 * 4^2

Area = 50.24

Area of the colored portion 2 * 1/6 * pi * r^2 = 16.75

Area of the white part of the circle = 50.24 - 16.75 = 33.49

Interlude

Here is what you are doing. You are taking the area of the entire circle and then you are using the area of the white part of the circle. The point has to be either in the red part or the white part. There is no where else it can go. Outside the circle doesn't count.

You now have the area of the white part (33.49) and that is divided by the area of the entire circle. That gives you the probability of landing on the white.  Computers love this kind of problem. If you ran this a million times, it would come pretty close to the answer.

Answer

P(white) = 33.49 / 50.24 = 2/3  which is what you think you should get just by eye balling it.

Discussion

The easier way of doing this is to take 1/2 + 1/6 = 3/6 + 1/6 = 2/3

The 1/2 is the white 1/2 circle. the 1/6 is a pizza slice that is 1/6 of the circle

Why didn't I do it that way? Because sometimes you get a question that is not that well behaved. The first method never fails. This method might not lend itself to an easy solution.

vbbv

step-by-step explanation: