If you remember the problem, the key is the fact that the problem never said to choose one of the answers from the multiple choice list. Also, the question never said that that question was the one that applied to the multiple choice questions. Having those two facts in mind, you now have to do the math and figure out what the odds actually are that you at least got the question “right in some way“. Since that phrase is used, “right in some way“, we can assume that more than one of the options are the answer. Knowing this, what are all of the possible answer permutations?

1. a
2. b
3. c
4. d
5. e
6. ab
7. ac
9. ae
10. bc
11. bd
12. be
13. cd
14. ce
15. de
16. abc
17. abd
18. abe
19. acd
20. ace
22. bcd
23. bce
24. bde
25. cde
26. abcd
27. abce
28. abde
29. acde
30. bcde
31. abcde

As shown above, we have 31 different answers that could be right. Since we have been limited to picking one letter at random, to determine the odds that your answer at least partially matches one of the answers listed above, you will have to multiply 31 by 5. That comes to 155 total possible scenarios. Now the final part of the problem is to determine how many of those times the random answer that is chosen would actually be correct. Since we can only pick one letter at random and it has to be one of the ones listed above, the number of characters that appear above is the same as the total amount of times that you will be correct. There are 80 letters shown above. In conclusion, the chance that you will at least be partially correct is 80 out of 155 or about 52%.

I know that many people probably disagree with me on this one, but in the end, since I wrote the problem, I am not sure I can be wrong on this one. 😉 Still, thanks for the feedback in advanced.