Statistics - Probability

QUESTION

If a new type of torch battery has a voltage that is outside certain limits, that battery is characterised as a failure (F); if the battery has a voltage within the prescribed limits, it is a success (S). Suppose an experiment consists of testing each battery as it comes off an assembly line until we first observe a success. Although it may not be very likely, a possible outcome of this experiment is that the first 10 (or 100 or 1000 or ..) are F’s and the next one is an S. That is, for any positive integer n, we may have to examine n batteries before seeing the first S. We can denote by FFS the outcome that we have to test n = 2 batteries before the first success.

(i) Write down 5 other outcomes in the sample space. How large is this sample space?

(ii) List the outcomes in the event that at most three batteries are examined.

(iii) List 3 outcomes in the event that an even number of batteries is examined.

ATTEMPT

(i) I know the sample space is the range of values of a random variable.

So could 5 other outcomes be: FS, FFFS, FFFFS, FFFFFS and FFFFFFS?

And would the size of the sample space be infinity since there is no limit?

(ii) Would this be: S, FS and FFS?

(iii) And would this be: FS, FFFS and FFFFFS?

Thanks!

• I think you're right. – SinTan1729 Feb 2 '16 at 16:40

1 Answer

With the problem as described, you are correct that the sample space consists of the outcomes where you observe any number of failures followed by a single success. Given that, all of your answers are correct: you're looking for the set of "Some number of Fs, followed by a single S" that matches the given requirements: (i) any 5 such strings, (ii) strings with length 3 or less, (iii) strings with even length.