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?

Correct Option (B)

To guarantee picking at least one ball of each colour, the worst-case scenario must be considered. This scenario involves picking all balls of the two most numerous colours before any ball of the third colour is selected.

• The number of green balls is 8.
• The number of white balls is 7.
• The number of red balls is 5.

The two most numerous colours are green (8 balls) and white (7 balls). In the worst-case, one would pick all 8 green balls and all 7 white balls first. The total number of balls picked in this scenario would be 8 + 7 = 15 balls.

After picking these 15 balls, it is possible that no red ball has been picked. Therefore, the very next ball picked (the 16th ball) must be a red ball, thereby ensuring that at least one ball of each colour (green, white, and red) is present among the picked balls.

Incorrect Options:

• Option A (17): Picking 17 balls would certainly assure at least one of each colour, as this assurance is already met with 16 balls. Therefore, 17 is not the minimum number required.

• Option C (13): Picking 13 balls does not guarantee one of each colour. For instance, one could pick all 8 green balls and all 5 red balls (8 + 5 = 13 balls), in which case no white ball would have been picked. Alternatively, one could pick all 8 green balls and 5 white balls, missing red.

• Option D (11): Picking 11 balls is insufficient. For example, one could pick all 8 green balls and 3 white balls (8 + 3 = 11 balls), resulting in no red ball and an insufficient number of white balls to exhaust that colour, let alone guarantee all three colours.