# Bernoulli or Geometric Distribution

• July 2nd 2011, 06:12 PM
itpro
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.
• July 2nd 2011, 06:29 PM
TKHunny
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.
• July 2nd 2011, 09:47 PM
chisigma
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...

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

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

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

Kind regards

$\chi$ $\sigma$