Question

Consider three positive integers, x1, x2, x3, which satisfy the inequality below:
x1 + x2 + x3 = 17.
Let’s assume each element in the sample space (consisting of solution vectors (x1, x2, x3) satisfying the above conditions) is equally likely to occur. For example, we have equal chances to have (x1, x2, x3) = (1, 1, 15) or (x1, x2, x3) = (1, 2, 14). What is the probability the events x1 + x2 ≤ 8 occurs, i.e., P(x1 + x2 ≤ 8 | x1 + x2 + x3 = 17 and x1, x2, x3 ∈ Z+) (Z+ is the set containing all the possible positive integers)?

Answer 1