A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. What is the minimum number of balls that must be picked up from the bag blindfolded (without replacing any of it) to be assured of picking at least one ball of each colour?

The correct option is 16.

To find the minimum number of balls that must be picked to be guaranteed of getting at least one ball of each colour, we need to consider the worst-case scenario.

Let us note the number of balls of each colour present in the bag:
Green balls = 8
White balls = 7
Red balls = 5
Total number of balls = 20

In the worst-case scenario, we pick all the balls of the two colors with the maximum counts before getting a single ball of the remaining third color.

The two colors with the highest number of balls are:
Green (8 balls) and White (7 balls).

If we are very unlucky, we might draw all 8 green balls and all 7 white balls consecutively without drawing any red ball.

Number of balls picked so far = 8 (Green) + 7 (White) = 15 balls.

At this point, 15 balls have been picked, and only red balls are left in the bag. Therefore, the very next ball (the 16th ball) picked from the bag is guaranteed to be a red ball.

$\text{Minimum number of balls required}=8+7+1=16$

Thus, picking a minimum of 16 balls ensures that we have at least one ball of each colour.