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# Statistics Problem. Watch

1. Greetings, I was solving a probability exercise from a Stats pastpaper and I got stuck in 1 mark question.

Erika is a birdwatcher. The probability that she will see a woodpecker on any given day is 1/8. It is assumed that this probability is unaffected by whether she has seen a woodpecker on any other day.

i) Calculate the probability that Erika first sees a woodpecker

(a) on the third day [3] - I got 49/512 which is right

(b) after the third day [3] I got 343/512 which is right

ii) Find the expectation of the number of days up to and including the first day on which she sees woodpecker [1]

I don't know how to calculate E(X) without knowing how many times she will go. Or maybe they're asking for something else?
2. (Original post by Blackfyre)
Greetings, I was solving a probability exercise from a Stats pastpaper and I got stuck in 1 mark question.

Erika is a birdwatcher. The probability that she will see a woodpecker on any given day is 1/8. It is assumed that this probability is unaffected by whether she has seen a woodpecker on any other day.

i) Calculate the probability that Erika first sees a woodpecker

(a) on the third day [3] - I got 49/512 which is right

(b) after the third day [3] I got 343/512 which is right

ii) Find the expectation of the number of days up to and including the first day on which she sees woodpecker [1]

I don't know how to calculate E(X) without knowing how many times she will go. Or maybe they're asking for something else?
How did you work out a and b ?
3. (Original post by zed963)
How did you work out a and b ?
I used tree diagram for both.

a) 7/8*7/8*1/8
b) (7/8)^3
4. Bump, still need help.
5. (Original post by Blackfyre)
Bump, still need help.

PS: You should recognise the distribution, in which case you may be able to just quote the result, rather than use first principles.

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Updated: April 17, 2014
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