If we leave one question blank and choose an option randomly for the other 9 questions, the probability of getting a positive score will be approximately 70 percent, which is better than guessing all the questions (in which case the probability of a positive score is approximately 47 percent).

If we randomly choose an option for \(n\) questions and leave the rest blank, the probability of answering exactly \(c\) questions correctly is \(\binom{n}{c} 0.25^c 0.75^{n-c}\). To get a positive score on 9 questions, we need to answer at least 2 questions correctly. So the probability of getting a positive score with 9 questions is \[1 - \binom{10}{0} 0.75^{10} - \binom{10}{1} 0.25 0.75^{9}\] which is approximately 0.70. Table below shows the probability that we get a positive score by making a guess on a certain number of questions.

Number of Questions to be Guessed	Number of Correct Answers Needed	Probability of a Positive Score
1	1	0.25
2	1	0.44
3	1	0.58
4	1	0.68
5	2	0.37
6	2	0.47
7	2	0.56
8	2	0.63
9	2	0.70
10	3	0.47

As you can see, the best strategy is to leave a question black and guess the answer for the rest of the questions.