Bernoulli or Geometric Distribution

Would you advise me please on what is appropriate distribution calculation here

and how to set it up:

An unbiased coin is tossed repeatedly until a “tail” is observed for the second time.

Find the probability that it would require k tosses to achieve that

**Disclamer:**

This is a practice problem for entrance exam, and not a homework. If confirmation is needed send e-mail and I will send link to a problem on the web.

Re: Bernoulli or Geometric Distribution

Since a Bernoulli Distribution is defined only for a single experiment (one toss, in this case), this rather rules out the Bernoulli.

Re: Bernoulli or Geometric Distribution

Quote:

Originally Posted by

**itpro** Would you advise me please on what is appropriate distribution calculation here

and how to set it up:

An unbiased coin is tossed repeatedly until a “tail” is observed for the second time.

Find the probability that it would require k tosses to achieve that

**Disclamer:**

This is a practice problem for entrance exam, and not a homework. If confirmation is needed send e-mail and I will send link to a problem on the web.

The probability of 'one tail in k-1 trials' is...

$\displaystyle P_{k-1}= \binom{k-1}{1}\ p\ (1-p)^{k-2}= (k-1)\ 2^{1-k}$ (1)

... so that the requested probability is...

$\displaystyle P_{k}= (k-1)\ 2^{-k}$ (2)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$