The internal evaluation for Economics course in an Engineering programme is based on the score of four quizzes. Rahul has secured 70, 90 and 80 in the first three quizzes. The fourth quiz has ten True-False type questions, each carrying 10 marks. What is the probability that Rahul’s average internal marks for the Economics course is more than 80, given that he decides to guess randomly on the final quiz?

- 12/1024
- 11/1024
- 11/256
- 12/256

**Solution**

Average marks in first three quizzes = 80

So, to have average internal marks more than 80, he has to score more than 80 marks in the fourth quiz. This is possible if he attempts 9 or 10 questions correctly.

Number of ways this can be done = 1 + ^{10}C_{9} = 1 + 10 = 11

Total number of ways the quiz can be solved = 2^{10} = 1024

Required probability = 11/1024

**The correct option is B.**