Answer:To find out the theoretical probability of the case given, we need to make certain assumptions.
First, we'll assume that he'll attempt all of the questions, i.e he'll attempt all 10 questions.
Next assumption is that each option in each question is equally likely to be marked by the student.
This pretty much leads us to a binomial probability distribution.
Conditions are:
Answers 10 questions.
Each question has 4 options with only one correct answer and all other incorrect answers.
Student is equally likely to pick any outcome in any given question.
Hence, probability of choosing correct answer is 1/4 = 0.25. Probability of choosing incorrect answer is 1–1/4 = 3/4 = 0.75.
The number of trials is 10.
Total number of success is exactly 8 and failure is 2 amongst the 10 questions in any particular order.
Now, calculation is fairly simple.
Binomial probability distribution is such that…
P(8 correct ; 2 wrong)
= 10C8 × (0.25)^8 × (0.75)²
= 405/1048576 ≈ 3.862380981 × 10^-4 ≈ 0.000386
Step-by-step explanation:
