A student earned 3 points. To pass exam, the student needs to accumulate 8 points. The student can bet any number of points n > 0 (n ∈ ℝ) (n <= X with X being the current number of points). If they solve a problem correctly (probability 0.4), they gain n points otherwise, they lose n points. If the student’s total reaches 0, they fail and must retake the exam later.
What is the optimal betting strategy for the student, and what is the probability of passing under this strategy?
What is the optimal betting strategy for the student, and what is the probability of passing under this strategy?
