Chapter 3 : 3.12 - Exercises Problem 7

[Sahil Khan]

The solution given by you here seems incorrect to me. There should be (1-px) term in the end to account for failing.

Refer - math.stackexchange

[vmdd]

I guess you meant this problem (or the link might have changed).

For the case of only reaching lvl 1 and no futher, we need to account for failure to go to lvl2 $(1 - p_1)$, so

$$P(X = 1) = 1 \cdot (1 - p_1)$$

Also, it cannot be equal $1$ at $X = 1$, since that would mean it needs to be $0$ at any other point.