Geometric Distribution Probability problem

[Hiche]

Homework Statement

We roll a fair die until we get a three or a four. Z denotes the number of rolls needed. What is the probability that Z >= 3? (replacement assumed)

Homework Equations

Geometric distribution seems logical here?

The Attempt at a Solution

Let p(A) = p(getting a three) = 1/6 and p(B) = p(getting a four) = 1/6. We want p(A U B) = 1/3 (a three OR a four). Correct?

Now, we know p(Z >= k) = (1 - p)^(k - 1). Is that enough for this question? I got 4/9.

 

[tiny-tim]

Hi Hiche!

Yes, 4/9.

Probably best to specifically say that Z ≥ 3 means that there is no 3 or 4 in the first two rolls, the probability of which is P(not A or B) squared.