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 blind-folded (without replacing any of it) to be assured of picking at least one ball of each colour?
- A4
- B7
- C11
- D16Correct
Explanation
To ensure you have at least one ball of each color, you must consider the worst case scenario. In this scenario, you keep picking balls of the same colors until those colors are completely exhausted before you finally pick a ball of the remaining color.
The bag contains 8 green, 7 white, and 5 red balls.
The worst case would be picking all 8 green balls and all 7 white balls first. At this point, you have picked 15 balls but still do not have a red ball. The very next ball you pick, which is the 16th ball, must be red because only red balls are left in the bag.
Calculation: 8 green + 7 white + 1 red = 16 balls.
By picking 16 balls, you are guaranteed to have at least one ball of each color. Therefore, the correct answer is 16.
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