Finding the probability mass function of

Question

Consider an information source that produces numbers k in the set SX = {1, 2, 3, 4}. Find and plot the PMF in the following cases:

(a) p_k = p₁/k, for k = 1, 2, 3, 4. Hint: Find p₁.

I attempted to solve this problem by doing the following.

p₁/1+ p₁/2 + p₁/3 +p₁/4 =1.

Solving for p1 I got p1 = 12/25 and the PMF to be 12/25k.

However the professor claims that it is p1=8/15. could someone please explain how 8/15 could be the correct answer? The professor's solution can be found at the following link.

https://youtu.be/aWxW9zey1RU?si=6SBn1OyxvrIe0Egb