Since there are seventeen different pairs of socks, it should be obvious that you can take seventeen socks out of the basket without getting a matched pair.
The dry cleaner just delivered seventeen freshly cleaned different pairs of socks in a basket but the light bulb went out. The dry cleaner did not match the socks before delivery and I am in a hurry, so I blindly pick single socks from the basket. Is it possible that I actually will be wearing a matching pair of socks that evening after ten picks and how many times do I have to reach into that basket minimally to be guaranteed a matching pair of socks?
1. No, you have to pick at least 18 times from the basket to have a matching pair of socks.
2. No, you have to pick at least three times from the basket to have a matching pair of socks.
3. Yes, you have to pick at least two times from the basket to have a matching pair of socks. This is not very likely though.
4. Yes, you have to pick at least one time from the basket to have a matching pair of socks. This is not very likely though.
5. None of the above
what would be the best option?
After picking the 1st single sock, remains 33 single socks. Now you start picking a 2nd single sock, if not as 1st then put it aside and pick 3rd single sock....repeating this 10 times for single sock=2,3,....11 we have the following increasing probabilities of picking the matching single sock to 1st sock:
these 10 picks sums to 0.3545 probability of finding the matching single sock.