Is this a poorly written question?

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Let X a be a random variable. P[x=0]=.55

For every i >= 0 , P[x=i+1] = 1/3 P[ x=i ]

Find P[ x<=2 ]

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The answer given (without explanation) is .825, but it is not the answer that I have problems with, it is the question itself. Here is what I am thinking.

X is obviously a Geometric Random Variable. Because it gives the probability for x=0, the distribution must have the form

P[X=x]= q^x * p

That means that P[x=0] = p which implies that p = .55

But they then say that the probability of q is 1/3. (Right? If every probability of x+1 is 1/3 x?)

Any thoughts?

Thanks

----

Let X a be a random variable. P[x=0]=.55

For every i >= 0 , P[x=i+1] = 1/3 P[ x=i ]

Find P[ x<=2 ]

----

The answer given (without explanation) is .825, but it is not the answer that I have problems with, it is the question itself. Here is what I am thinking.

X is obviously a Geometric Random Variable. Because it gives the probability for x=0, the distribution must have the form

P[X=x]= q^x * p

That means that P[x=0] = p which implies that p = .55

But they then say that the probability of q is 1/3. (Right? If every probability of x+1 is 1/3 x?)

Any thoughts?

Thanks

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