Q66 2017, Probability

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?

एक थैले में 20 गेंदें हैं। 8 गेंदें हरी हैं, 7 सफ़ेद हैं और 5 लाल हैं। आँख बंद कर, थैले में से न्यूनतम कितनी गेंदें निकालना आवश्यक है (किसी को भी बिना बदले) जिससे सुनिश्चित हो कि प्रत्येक रंग की कम-से-कम एक गेंद निकली हो?

A bag contains 20 balls. 8 balls are green, 7 are white and 5 are red. We have to pick at least one ball of each colour.

Now consider this: Even if we pick 8 balls, there’s a probability that all of them may be green. Hence, we must pick more than 8 balls for sure.

Now, even if we pick 8 + 7 balls, i.e. 15 balls, there’s a probability that all of them may be green and white only, with no red ball picked at all.

Hence, taking the worst possible scenario in consideration we must pick 15 + 1 = 16 balls to be sure that atleast one ball of all the three colours is picked.