To find the probability of randomly choosing a ball that is not green (P(Gc)), we need to first calculate the total number of balls in the bag that are not green and then divide it by the total number of balls in the bag.
Step 1: Calculate the total number of balls that are not green.
In this case, we have 7 yellow balls and 3 red balls which are not green. Adding them together, we get 7 + 3 = 10 balls that are not green.
Step 2: Calculate the total number of balls in the bag.
From the information given, we know there are 7 yellow balls, 3 red balls, and 6 green balls. So the total number of balls in the bag is 7 + 3 + 6 = 16.
Step 3: Calculate the probability.
Now that we have the total number of balls that are not green (10) and the total number of balls (16), we can calculate the probability of randomly choosing a ball that is not green:
P(Gc) = Number of balls that are not green / Total number of balls
P(Gc) = 10 / 16
Simplifying the fraction, we get:
P(Gc) = 5/8
Therefore, the probability of randomly choosing a ball that is not green is 5/8.