Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make?

Question

Accepted Answer

The correct answer is option D. This is a worst-case scenario problem. To guarantee a red pair, Raj must first pick all shoes that are not red, and then enough red shoes to ensure a pair (one left, one right). There are 10 pairs of red (20 shoes), 9 pairs of white (18 shoes), and 8 pairs of black (16 shoes). In the worst case, Raj would first pick all the white shoes (18 attempts) and all the black shoes (16 attempts). This totals 18 + 16 = 34 shoes, none of which are red. At this point, only red shoes remain in the box. To guarantee a red pair, he could then pick all 10 left red shoes (worst case, assuming he picks all of one type first). The very next shoe he picks (the 11th red shoe) must be a right red shoe, completing a pair. So, the maximum number of attempts = 34 (non-red shoes) + 10 (all left red shoes) + 1 (one right red shoe) = 45 attempts. This question tests logical thinking and the application of the worst-case scenario principle, a common type in CSAT.

Q34. Raj has ten pairs of red, nine pairs of white and eight pairs of black shoes in a box. If he randomly picks shoes one by one (without replacement) from the box to get a red pair of shoes to wear, what is the maximum number of attempts he has to make?

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