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Most probable sum - 2015 PAMO Problem 5

Source: 2015 Pan-African Mathematics Olympiad Problem 5

August 26, 2015
combinatoricsprobability

Problem Statement

There are seven cards in a hat, and on the card kk there is a number 2kāˆ’12^{k-1}, k=1,2,...,7k=1,2,...,7. Solarin picks the cards up at random from the hat, one card at a time, until the sum of the numbers on cards in his hand exceeds 124124. What is the most probable sum he can get?
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