Memory Match Problem #1
You and your friend are playing a memory match game in which 50 different pairs of cards (100 total) are thoroughly mixed up and placed face down on the table. You and your friend each take turns turning over 2 cards at a time, attempting to obtain a matching pair. Your friend says you can go first.
On this first turn, what is the probability that you turn over a matching pair by choosing 2 cards at random?
Details and Assumptions:
- The cards are distributed completely randomly across the table.
- You have no extra or prior knowledge of the location of any of the cards.
This problem is a part of the Memory Match Problem Series
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1 solution
To find the probability of choosing a matching pair at random, we need only consider the second card chosen. This is because the second card is what will determine whether or not the pair is a match.
Once the first card is chosen, there will be 99 cards left. Out of these 99, we must find the one card which matches the first. Thus, the probability of choosing this second card, and therefore the matching pair, is 9 9 1 .